ÁLGEBRA 1/3. GEOMETRÍA ANALÍTICA
GEO. ANALÍTICA.03. Dada la ecuación de una elipse, determinar la gráfica
La gráfica del lugar geométrico que representa la ecuación #ec es: ]]>
1.0000000
1.0000000
0
true
true
abc
#opa]]>
#retropersonal]]>
#opb]]>
Al parecer no identificaste correctamente la gráfica y su ecuación.]]>
#opc]]>
Al parecer no identificaste correctamente la gráfica y su ecuación. ]]>
#opd]]>
Al parecer no identificaste correctamente la gráfica y su ecuación. ]]>
<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><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><msup><mo>)</mo><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><msup><mo>)</mo><mn>2</mn></msup></mtd></mtr></mtable><mrow><mi>a1</mi><mo>></mo><mi>b1</mi></mrow></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>z1</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>z2</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"><mi>z3</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>z4</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"><mi>r1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ecuaciones</mi><mo> </mo><mi>a</mi><mo> </mo><mi>mostrar</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><mfrac><msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><msup><mfenced><mrow><mo>#</mo><mn>3</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>z1</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>z2</mi><mo>,</mo><mi>b1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><mfrac><msup><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><msup><mfenced><mrow><mo>#</mo><mn>3</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>z3</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>z4</mi><mo>,</mo><mi>b1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><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><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>z1</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>z2</mi><mo>,</mo><mi>b1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><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><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>z3</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>z4</mi><mo>,</mo><mi>b1</mi><mo>)</mo></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>R1</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mi>w1</mi><mo>,</mo><mn>2</mn><mo>→</mo><mi>w2</mi><mo>,</mo><mn>3</mn><mo>→</mo><mi>w3</mi><mo>,</mo><mn>4</mn><mo>→</mo><mi>w4</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec</mi><mo>=</mo><mi>R1</mi><mo>(</mo><mi>r1</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ecuaciones</mi><mo> </mo><mi>a</mi><mo> </mo><mi>graficar</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R2</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mfenced><mrow><mfrac><msup><mi>z1</mi><mn>2</mn></msup><mi>a1</mi></mfrac><mo>+</mo><mfrac><msup><mi>z2</mi><mn>2</mn></msup><mi>b1</mi></mfrac><mo>=</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mn>2</mn><mo>→</mo><mfenced><mrow><mfrac><msup><mi>z3</mi><mn>2</mn></msup><mi>a1</mi></mfrac><mo>+</mo><mfrac><msup><mi>z4</mi><mn>2</mn></msup><mi>b1</mi></mfrac><mo>=</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mn>3</mn><mo>→</mo><mfenced><mrow><mfrac><msup><mi>z2</mi><mn>2</mn></msup><mi>a1</mi></mfrac><mo>+</mo><mfrac><msup><mi>z1</mi><mn>2</mn></msup><mi>b1</mi></mfrac><mo>=</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mn>4</mn><mo>→</mo><mfenced><mrow><mfrac><msup><mi>z4</mi><mn>2</mn></msup><mi>a1</mi></mfrac><mo>+</mo><mfrac><msup><mi>z3</mi><mn>2</mn></msup><mi>b1</mi></mfrac><mo>=</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mn>5</mn><mo>→</mo><mfenced><mrow><mfrac><msup><mi>z1</mi><mn>2</mn></msup><mi>a1</mi></mfrac><mo>+</mo><mfrac><msup><mi>z2</mi><mn>2</mn></msup><mi>b1</mi></mfrac><mo>=</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mn>6</mn><mo>→</mo><mfenced><mrow><mfrac><msup><mi>z3</mi><mn>2</mn></msup><mi>a1</mi></mfrac><mo>+</mo><mfrac><msup><mi>z4</mi><mn>2</mn></msup><mi>b1</mi></mfrac><mo>=</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mn>7</mn><mo>→</mo><mfenced><mrow><mfrac><msup><mi>z2</mi><mn>2</mn></msup><mi>a1</mi></mfrac><mo>+</mo><mfrac><msup><mi>z1</mi><mn>2</mn></msup><mi>b1</mi></mfrac><mo>=</mo><mn>1</mn></mrow></mfenced><mo>}</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Elementos</mi><mo> </mo><mi>del</mi><mo> </mo><mi>tablero</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></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>r1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>C11</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C12</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mo>-</mo><mi>h1</mi><mo>,</mo><mo>-</mo><mi>k1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C13</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C14</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mo>-</mo><mi>h1</mi><mo>,</mo><mo>-</mo><mi>k1</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>r1</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>C14</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C11</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mo>-</mo><mi>h1</mi><mo>,</mo><mo>-</mo><mi>k1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C12</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C13</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mo>-</mo><mi>h1</mi><mo>,</mo><mo>-</mo><mi>k1</mi><mo>)</mo></mtd></mtr></mtable><mrow><mi>r1</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>C13</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C14</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mo>-</mo><mi>h1</mi><mo>,</mo><mo>-</mo><mi>k1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C11</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C12</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mo>-</mo><mi>h1</mi><mo>,</mo><mo>-</mo><mi>k1</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>C12</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C13</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mo>-</mo><mi>h1</mi><mo>,</mo><mo>-</mo><mi>k1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C14</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>h1</mi><mo>,</mo><mi>k1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>C11</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mo>-</mo><mi>h1</mi><mo>,</mo><mo>-</mo><mi>k1</mi><mo>)</mo></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>al</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>max</mi><mo>(</mo><mfenced close="|" open="|"><mi>h1</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>k1</mi></mfenced><mo>,</mo><msqrt><mi>a1</mi></msqrt><mo>,</mo><msqrt><mi>b1</mi></msqrt><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>al</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>{</mo><mi>centro</mi><mo>=</mo><mi>C11</mi><mo>,</mo><mi>altura</mi><mo>=</mo><mi>al</mi><mo>,</mo><mi>anchura</mi><mo>=</mo><mi>an</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>{</mo><mi>centro</mi><mo>=</mo><mi>C12</mi><mo>,</mo><mi>altura</mi><mo>=</mo><mi>al</mi><mo>,</mo><mi>anchura</mi><mo>=</mo><mi>an</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>{</mo><mi>centro</mi><mo>=</mo><mi>C13</mi><mo>,</mo><mi>altura</mi><mo>=</mo><mi>al</mi><mo>,</mo><mi>anchura</mi><mo>=</mo><mi>an</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>{</mo><mi>centro</mi><mo>=</mo><mi>C14</mi><mo>,</mo><mi>altura</mi><mo>=</mo><mi>al</mi><mo>,</mo><mi>anchura</mi><mo>=</mo><mi>an</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gr1</mi><mo>=</mo><mi>R2</mi><mo>(</mo><mi>r1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gr2</mi><mo>=</mo><mi>R2</mi><mo>(</mo><mi>r1</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gr3</mi><mo>=</mo><mi>R2</mi><mo>(</mo><mi>r1</mi><mo>+</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gr4</mi><mo>=</mo><mi>R2</mi><mo>(</mo><mi>r1</mi><mo>+</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>opa</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mi>gr1</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>azul</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>opb</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t2</mi><mo>,</mo><mi>gr2</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>azul</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>opc</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t3</mi><mo>,</mo><mi>gr3</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>azul</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>opd</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>t4</mi><mo>,</mo><mi>gr4</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>azul</mi><mo>}</mo><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Retroalientación</mi><mo>:</mo></math></comment></maction><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>ec</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup><mn>64</mn></mfrac><mo>+</mo><mfrac><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mn>2</mn></msup><mn>25</mn></mfrac><mo>=</mo><ms>1</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>4</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>4</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C14</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero4</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t5</mi></math></output></command></group><group><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><options><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="casSession"/></localData></question>