Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

A parabola can be drawn given a focus of (-5, -4)(−5,−4) and a directrix of y=-6y=−6. Write the equation of the parabola in any form.
screenshot below-

A Parabola Can Be Drawn Given A Focus Of 5 454 And A Directrix Of Y6y6 Write The Equation Of The Parabola In Any Form Screenshot Below class=

Sagot :

VectorFundament120

Answer:

[tex]\displaystyle \large{y=\dfrac{x^2}{4} + \dfrac{5x}{2} + \dfrac{5}{4}}[/tex]

Step-by-step explanation:

Given:

  • Focus = (-5,-4)
  • Directrix = -6

To find:

  • Parabola Equation

Locus of Parabola (Upward/Downward)

[tex]\displaystyle \large{\sqrt{(x-a)^2+(y-b)^2} = |y-c|}[/tex]

Where:

  • (a,b) = focus
  • c = directrix

Hence:

[tex]\displaystyle \large{\sqrt{(x+5)^2+(y+4)^2}=|y+6|}[/tex]

Cancel square root by squaring both sides as we get:

[tex]\displaystyle \large{(x+5)^2+(y+4)^2=(y+6)^2}[/tex]

Solve for y-term:

[tex]\displaystyle \large{(x+5)^2=(y+6)^2-(y+4)^2}\\\displaystyle \large{x^2+10x+25=y^2+12y+36-y^2-8y-16}\\\displaystyle \large{x^2+10x+25=4y+20}\\\displaystyle \large{x^2+10x+5=4y}\\\displaystyle \large{y=\dfrac{x^2}{4} + \dfrac{5x}{2} + \dfrac{5}{4}}[/tex]

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.