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

Answer:

$y^{2}=-16x$

Step-by-step 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

$(y-0)^{2}=4(-4)(x-0)$

$y^{2}=-16x$