Question

Write an equation of a parabola that opens to the left, has a vertex at the origin, and a focus at (–4, 0).

Answer 1

`y^(2)=-16x`

Explanation:

we know that

The standard equation of a horizontal parabola is equal to

`(y-k)^(2)=4p(x-h)`

where

(h,k) is the vertex

(h+p,k) is the focus

In this problem we have

(h,k)=(0,0) ----> vertex at origin

(h+p,k)=(-4,0)

so

h+p=-4

p=-4

substitute the values

`(y-0)^(2)=4(-4)(x-0)`

`y^(2)=-16x`