1MA 06. LLOCS GEOMÈTRICS/1MA.06.3 Còniques 1MA1.06.3.41Q EqParàbola Troba l'equació de la paràbola de focus situat en el punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math» i de directriu «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: y²=4x+15

]]> El gràfic és #G

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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>p</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>aleatori</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>m</mi><mo>=</mo><mfrac><mi>p</mi><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mo>-</mo><mfrac><mi>p</mi><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>4</mn><mo>*</mo><mi>m</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>sol</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_línia</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>verd</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>x</mi><mo>=</mo><mi>n</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_línia</mi><mo>=</mo><mn>3</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>vermell</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mi>m</mi><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mida_punt</mi><mo>=</mo><mn>5</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>vermell</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>4</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</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="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La distància d'un punt qualsevol P(x,y) al focus «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=91190ac5fb33bd271ad84922608f880b&cw=52&ch=13&cb=10" style="vertical-align: -3px;"/> és el mòdul del vector que els uneix: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#0000FF¨»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=9ce0c6649081ec60fb2bc83443c34853&cw=105&ch=20&cb=16" style="vertical-align: -4px;"/>

La distància d'un punt qualsevol P(x,y) a la recta d'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=d8b7c64b9b656d9760172084baaf3535&cw=72&ch=10&cb=9" style="vertical-align: -1px;"/> es calcula amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfenced»«msqrt»«mn mathvariant=¨bold¨»1«/mn»«/msqrt»«/mfrac»«/mstyle»«/math»" src="http://www.insmilaifontanals.cat/moodle/lib/editor/tinymce/plugins/tiny_mce_wiris/tinymce/integration/showimage.php?formula=d9f2d440459548d4b453aa6281776b84&cw=47&ch=32&cb=18" style="vertical-align: -14px;"/>

S'igualen les dues expressions i s'eleva al quadrat per treure l'arrel.

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