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High School
Geometry
High school geometry
Analytic geometry

nuais6lfp

Answered question

2021-11-26

Find the equation of the parabola with vertex (-2, 5) and focus (-4, 5). (10 points)

Answer & Explanation

huckelig75

Beginner2021-11-27Added 11 answers

Step1
Given the vertex (-2,5) and focus (-4,5) of a parabola
To find the equation of the parabola
It is clear that focus and vertex lie on the same horizontal line y=5
Also, the focus lies to the left of the vertex So it is clear that the parabola will open left.
Since the y coordinates are the same, the distance between the vertex and focus is given

a = - 2 - (- 4) = - 2 + 4 = 2

Step2
‘The equation of the parsbols is given by

(x - h^{2}) = - 4 a (y - k)

We have vertex (h,k)=(-2,5) and 3-2, then

{(x - (- 2))}^{2} = - 4 a (y - 5)

{(x + 2)}^{2} = - 4 (2) (y - 5)

{(x + 2)}^{2} = - 8 (y - 5)

This gives the equation of the parabola.

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