ÁLGEBRA 1/3. GEOMETRÍA ANALÍTICA GEO. ANALÍTICA.12. Dada una hipérbola en forma algebraica, determinar elementos

Dada la ecuación de la hipérbola «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»h«/mi»«mi»i«/mi»«mi»p«/mi»«mi»e«/mi»«mi»r«/mi»«/math» , determina las coordenadas de los focos, los vértices y asíntotas de la hipérbola.

Obs:

1) Escribe las coordenadas de los focos y de los vértices de la forma «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«mo»)«/mo»«/math» .

2) Si la hipérbola es horizontal considera como Foco 1 el de la derecha y como Foco 2 el de la izquierda, como Vértice 1 el de la derecha y como Vértice 2 el de la izquierda.

3) Si la hipérbola es vertical considera como Foco 1 al de arriba y como Foco 2 al de abajo, como Vértice 1 al de arriba y como Vértice 2 al de abajo.

4) Escribe las asíntotas de la forma «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«/math» , considera como Asíntota 1 la de pendiente positiva y como Asíntota 2 la de pendiente negativa.

]]> 1.0000000 0.3333333 0 0 Foco 1 = #SOL1Foco 2 = #SOL2Vertice 1 = #SOL3Vertice 2 = #SOL4Asintota 1= #SOL5Asintota 2 = #SOL6]]> #retropersonal

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h1</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><msup><mi>a1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msup><mi>b1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msqrt><mrow><mi>a2</mi><mo>+</mo><mi>b2</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h2</mi><mo>=</mo><mfenced close="|" open="|"><mi>h1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>h1</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>d1</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>d1</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><mfenced close="|" open="|"><mi>k1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo><</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>d2</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>d2</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>h1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>k1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>h1</mi><mo>=</mo><mn>0</mn><mo>∧</mo><mi>k1</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>hip_1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mfrac><msup><mi>x</mi><mn>2</mn></msup><mrow><mo>#</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><msup><mi>y</mi><mn>2</mn></msup><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mo>"</mo><mo>,</mo><mi>a2</mi><mo>,</mo><mi>b2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>hip_2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mfrac><msup><mi>y</mi><mn>2</mn></msup><mrow><mo>#</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><msup><mi>x</mi><mn>2</mn></msup><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mo>"</mo><mo>,</mo><mi>a2</mi><mo>,</mo><mi>b2</mi></mrow></mfenced></mtd></mtr></mtable><mrow><mi>h1</mi><mo>=</mo><mn>0</mn><mo>∧</mo><mi>k1</mi><mo>≠</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>hip_1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mfrac><msup><mi>x</mi><mn>2</mn></msup><mrow><mo>#</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><msup><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mo>"</mo><mo>,</mo><mi>a2</mi><mo>,</mo><mi>b2</mi><mo>,</mo><mi>w2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>hip_2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mfrac><msup><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup><mrow><mo>#</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><msup><mi>x</mi><mn>2</mn></msup><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mo>"</mo><mo>,</mo><mi>a2</mi><mo>,</mo><mi>b2</mi><mo>,</mo><mi>w2</mi></mrow></mfenced></mtd></mtr></mtable><mrow><mi>k1</mi><mo>=</mo><mn>0</mn><mo>∧</mo><mi>h1</mi><mo>≠</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>hip_1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mfrac><msup><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup><mrow><mo>#</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><msup><mi>y</mi><mn>2</mn></msup><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mo>"</mo><mo>,</mo><mi>a2</mi><mo>,</mo><mi>b2</mi><mo>,</mo><mi>w1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>hip_2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mfrac><msup><mi>y</mi><mn>2</mn></msup><mrow><mo>#</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mfrac><msup><mfenced><mrow><mo>#</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mo>"</mo><mo>,</mo><mi>a2</mi><mo>,</mo><mi>b2</mi><mo>,</mo><mi>w1</mi></mrow></mfenced></mtd></mtr></mtable><mtable><mtr><mtd><mi>hip_1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mfrac><msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mrow><mo>#</mo><mn>3</mn></mrow></mfrac><mo>-</mo><mfrac><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mrow><mo>#</mo><mn>4</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mo>"</mo><mo>,</mo><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>b2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>hip_2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mfrac><msup><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mrow><mo>#</mo><mn>3</mn></mrow></mfrac><mo>-</mo><mfrac><msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mrow><mo>#</mo><mn>4</mn></mrow></mfrac><mo>=</mo><mn>1</mn><mo>"</mo><mo>,</mo><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>b2</mi></mrow></mfenced></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hip_hor</mi><mo>=</mo><mfrac><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h1</mi></mrow></mfenced><mn>2</mn></msup><mi>a2</mi></mfrac><mo>-</mo><mfrac><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mi>k1</mi></mrow></mfenced><mn>2</mn></msup><mi>b2</mi></mfrac><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hip_ver</mi><mo>=</mo><mfrac><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mi>k1</mi></mrow></mfenced><mn>2</mn></msup><mi>a2</mi></mfrac><mo>-</mo><mfrac><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h1</mi></mrow></mfenced><mn>2</mn></msup><mi>b2</mi></mfrac><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>center</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>h1</mi><mo>,</mo><mi>k1</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ovh</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ovh</mi><mo>=</mo><mn>0</mn><mo>,</mo><mo> </mo><mi>hipérbola</mi><mo> </mo><mi>horizontal</mi><mo>,</mo><mo> </mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ovh</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo> </mo><mi>hipérbola</mi><mo> </mo><mi>vertical</mi><mo> </mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ovh</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>F1</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>+</mo><mi>c1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>F2</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>-</mo><mi>c1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>V1</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>+</mo><mi>a1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>V2</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>-</mo><mi>a1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>dir_1</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>y</mi><mo>-</mo><mi>k1</mi><mo>=</mo><mfrac><mi>a1</mi><mi>b1</mi></mfrac><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h1</mi></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>dir_2</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>y</mi><mo>-</mo><mi>k1</mi><mo>=</mo><mo>-</mo><mfrac><mi>a1</mi><mi>b1</mi></mfrac><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h1</mi></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>hiper</mi><mo>=</mo><mi>hip_2</mi></mtd></mtr><mtr><mtd><mi>tipo</mi><mo>=</mo><mo>"</mo><mi>vertical</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>F01</mi><mo>=</mo><mo>"</mo><mfenced><mrow><mi>h</mi><mo>,</mo><mi>k</mi><mo>+</mo><mi>c</mi></mrow></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>F02</mi><mo>=</mo><mo>"</mo><mfenced><mrow><mi>h</mi><mo>,</mo><mi>k</mi><mo>-</mo><mi>c</mi></mrow></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>V01</mi><mo>=</mo><mo>"</mo><mfenced><mrow><mi>h</mi><mo>,</mo><mi>k</mi><mo>+</mo><mi>a</mi></mrow></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>V02</mi><mo>=</mo><mo>"</mo><mfenced><mrow><mi>h</mi><mo>,</mo><mi>k</mi><mo>-</mo><mi>a</mi></mrow></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>as1</mi><mo>=</mo><mo>"</mo><mi>y</mi><mo>-</mo><mi>k</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h</mi></mrow></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>as2</mi><mo>=</mo><mo>"</mo><mi>y</mi><mo>-</mo><mi>k</mi><mo>=</mo><mo>-</mo><mfrac><mi>a</mi><mi>b</mi></mfrac><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h</mi></mrow></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>F03</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><msub><mi>F</mi><mn>1</mn></msub><mo>=</mo><mfenced><mrow><mo>#</mo><mn>1</mn><mo>,</mo><mo>#</mo><mn>2</mn><mo>+</mo><mo>#</mo><mn>3</mn></mrow></mfenced><mo>=</mo><mo>#</mo><mn>4</mn><mo>"</mo><mo>,</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>,</mo><mi>c1</mi><mo>,</mo><mi>F1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>F04</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><msub><mi>F</mi><mn>1</mn></msub><mo>=</mo><mfenced><mrow><mo>#</mo><mn>1</mn><mo>,</mo><mo>#</mo><mn>2</mn><mo>-</mo><mo>#</mo><mn>3</mn></mrow></mfenced><mo>=</mo><mo>#</mo><mn>4</mn><mo>"</mo><mo>,</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>,</mo><mi>c1</mi><mo>,</mo><mi>F2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>V03</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><msub><mi>F</mi><mn>1</mn></msub><mo>=</mo><mfenced><mrow><mo>#</mo><mn>1</mn><mo>,</mo><mo>#</mo><mn>2</mn><mo>+</mo><mo>#</mo><mn>3</mn></mrow></mfenced><mo>=</mo><mo>#</mo><mn>4</mn><mo>"</mo><mo>,</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>V1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>V04</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><msub><mi>F</mi><mn>1</mn></msub><mo>=</mo><mfenced><mrow><mo>#</mo><mn>1</mn><mo>,</mo><mo>#</mo><mn>2</mn><mo>-</mo><mo>#</mo><mn>3</mn></mrow></mfenced><mo>=</mo><mo>#</mo><mn>4</mn><mo>"</mo><mo>,</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>V2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>d_1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><msub><mi>L</mi><mn>1</mn></msub><mo>:</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mfenced><mrow><mi>x</mi><mo>#</mo><mn>3</mn><mo>#</mo><mn>4</mn></mrow></mfenced><mo>#</mo><mn>5</mn><mo>#</mo><mn>6</mn><mo>⇒</mo><msub><mi>L</mi><mn>1</mn></msub><mo>:</mo><mo>#</mo><mn>7</mn><mo>"</mo><mo>,</mo><mi>b1</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>d1</mi><mo>,</mo><mi>h2</mi><mo>,</mo><mi>d3</mi><mo>,</mo><mi>k2</mi><mo>,</mo><mi>dir_1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>d_2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><msub><mi>L</mi><mn>2</mn></msub><mo>:</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mfenced><mrow><mi>x</mi><mo>#</mo><mn>3</mn><mo>#</mo><mn>4</mn></mrow></mfenced><mo>#</mo><mn>5</mn><mo>#</mo><mn>6</mn><mo>⇒</mo><msub><mi>L</mi><mn>2</mn></msub><mo>:</mo><mo>#</mo><mn>7</mn><mo>"</mo><mo>,</mo><mi>b1</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>d1</mi><mo>,</mo><mi>h2</mi><mo>,</mo><mi>d3</mi><mo>,</mo><mi>k2</mi><mo>,</mo><mi>dir_2</mi></mrow></mfenced></mtd></mtr></mtable><mtable><mtr><mtd><mi>F1</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>h1</mi><mo>+</mo><mi>c1</mi><mo>,</mo><mi>k1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>F2</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>h1</mi><mo>-</mo><mi>c1</mi><mo>,</mo><mi>k1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>V1</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>h1</mi><mo>+</mo><mi>a1</mi><mo>,</mo><mi>k1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>V2</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>h1</mi><mo>-</mo><mi>a1</mi><mo>,</mo><mi>k1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>dir_1</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>y</mi><mo>-</mo><mi>k1</mi><mo>=</mo><mfrac><mi>b1</mi><mi>a1</mi></mfrac><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h1</mi></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>dir_2</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>y</mi><mo>-</mo><mi>k1</mi><mo>=</mo><mo>-</mo><mfrac><mi>b1</mi><mi>a1</mi></mfrac><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h1</mi></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>hiper</mi><mo>=</mo><mi>hip_1</mi></mtd></mtr><mtr><mtd><mi>tipo</mi><mo>=</mo><mo>"</mo><mi>horizontal</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>F01</mi><mo>=</mo><mo>"</mo><mfenced><mrow><mi>h</mi><mo>+</mo><mi>c</mi><mo>,</mo><mi>k</mi></mrow></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>F02</mi><mo>=</mo><mo>"</mo><mfenced><mrow><mi>h</mi><mo>-</mo><mi>c</mi><mo>,</mo><mi>k</mi></mrow></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>V01</mi><mo>=</mo><mo>"</mo><mfenced><mrow><mi>h</mi><mo>+</mo><mi>a</mi><mo>,</mo><mi>k</mi></mrow></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>V02</mi><mo>=</mo><mo>"</mo><mfenced><mrow><mi>h</mi><mo>-</mo><mi>a</mi><mo>,</mo><mi>k</mi></mrow></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>as1</mi><mo>=</mo><mo>"</mo><mi>y</mi><mo>-</mo><mi>k</mi><mo>=</mo><mfrac><mi>b</mi><mi>a</mi></mfrac><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h</mi></mrow></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>as2</mi><mo>=</mo><mo>"</mo><mi>y</mi><mo>-</mo><mi>k</mi><mo>=</mo><mo>-</mo><mfrac><mi>b</mi><mi>a</mi></mfrac><mfenced><mrow><mi>x</mi><mo>-</mo><mi>h</mi></mrow></mfenced><mo>"</mo></mtd></mtr><mtr><mtd><mi>F03</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><msub><mi>F</mi><mn>1</mn></msub><mo>=</mo><mfenced><mrow><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>3</mn><mo>,</mo><mo>#</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mo>#</mo><mn>4</mn><mo>"</mo><mo>,</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>,</mo><mi>c1</mi><mo>,</mo><mi>F1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>F04</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><msub><mi>F</mi><mn>1</mn></msub><mo>=</mo><mfenced><mrow><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>3</mn><mo>,</mo><mo>#</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mo>#</mo><mn>4</mn><mo>"</mo><mo>,</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>,</mo><mi>c1</mi><mo>,</mo><mi>F2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>V03</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><msub><mi>F</mi><mn>1</mn></msub><mo>=</mo><mfenced><mrow><mo>#</mo><mn>1</mn><mo>+</mo><mo>#</mo><mn>3</mn><mo>,</mo><mo>#</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mo>#</mo><mn>4</mn><mo>"</mo><mo>,</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>V1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>V04</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><msub><mi>F</mi><mn>1</mn></msub><mo>=</mo><mfenced><mrow><mo>#</mo><mn>1</mn><mo>-</mo><mo>#</mo><mn>3</mn><mo>,</mo><mo>#</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mo>#</mo><mn>4</mn><mo>"</mo><mo>,</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>V2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>d_1</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mfenced><mrow><mi>x</mi><mo>#</mo><mn>3</mn><mo>#</mo><mn>4</mn></mrow></mfenced><mo>#</mo><mn>5</mn><mo>#</mo><mn>6</mn><mo>⇒</mo><mo>#</mo><mn>7</mn><mo>"</mo><mo>,</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>d1</mi><mo>,</mo><mi>h2</mi><mo>,</mo><mi>d3</mi><mo>,</mo><mi>k2</mi><mo>,</mo><mi>dir_1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>d_2</mi><mo>=</mo><mi>sustituir_cadena</mi><mfenced><mrow><mo>"</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mfenced><mrow><mi>x</mi><mo>#</mo><mn>3</mn><mo>#</mo><mn>4</mn></mrow></mfenced><mo>#</mo><mn>5</mn><mo>#</mo><mn>6</mn><mo>⇒</mo><mo>#</mo><mn>7</mn><mo>"</mo><mo>,</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>d1</mi><mo>,</mo><mi>h2</mi><mo>,</mo><mi>d3</mi><mo>,</mo><mi>k2</mi><mo>,</mo><mi>dir_2</mi></mrow></mfenced></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL1</mi><mo>=</mo><mi>F1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL2</mi><mo>=</mo><mi>F2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL3</mi><mo>=</mo><mi>V1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL4</mi><mo>=</mo><mi>V2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL5</mi><mo>=</mo><mi>dir_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL6</mi><mo>=</mo><mi>dir_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>retropersonal</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>"</mo><mi>Bien</mi><mo>.</mo><mo> </mo><mi>Continúa</mi><mo> </mo><mi>de</mi><mo> </mo><mi>esa</mi><mo> </mo><mi>manera</mi><mo>.</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>¡</mo><mi>Muy</mi><mo> </mo><mi>bien</mi><mo>!</mo><mo> </mo><mi>Sigue</mi><mo> </mo><mi>así</mi><mo>.</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>¡</mo><mi>Excelente</mi><mo>!</mo><mo>"</mo><mo>,</mo><mo>"</mo><mi>Felicitaciones</mi><mo>,</mo><mo> </mo><mo>¡</mo><mi>muy</mi><mo> </mo><mi>bien</mi><mo>!</mo><mo>"</mo><mo>}</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tipo</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>vertical</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hiper</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mn>100</mn></mfrac><mo>-</mo><mfrac><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mn>64</mn></mfrac><mo>=</mo><ms>1</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>*</mo><msqrt><mn>41</mn></msqrt><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>*</mo><msqrt><mn>41</mn></msqrt><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mn>12</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>8</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>9</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>o</mi><mi>c</mi><mi>o</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>S</mi><mi>O</mi><mi>L</mi><mn>1</mn><mspace linebreak="newline"/><mi>F</mi><mi>o</mi><mi>c</mi><mi>o</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>S</mi><mi>O</mi><mi>L</mi><mn>2</mn><mspace linebreak="newline"/><mi>V</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi mathvariant="normal">e</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>S</mi><mi>O</mi><mi>L</mi><mn>3</mn><mspace linebreak="newline"/><mi>V</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi mathvariant="normal">e</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>S</mi><mi>O</mi><mi>L</mi><mn>4</mn><mspace linebreak="newline"/><mi>A</mi><mi>sin</mi><mi>t</mi><mi>o</mi><mi>t</mi><mi>a</mi><mo> </mo><mn>1</mn><mo>=</mo><mo> </mo><mo>#</mo><mi>S</mi><mi>O</mi><mi>L</mi><mn>5</mn><mspace linebreak="newline"/><mi>A</mi><mi>sin</mi><mi>t</mi><mi>o</mi><mi>t</mi><mi>a</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>S</mi><mi>O</mi><mi>L</mi><mn>6</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>