Question

What is the equation of a parabola with vertex at (1, −3) and focus at (−2, −3)?

Answer 1

A. (y + 3)^2 = −12(x + 2)
B. (y + 3)^2 = −4(x − 1)
C. (y + 3)^2 = 12(x − 1)
D. (y + 3)^2 = −12(x − 1)

Answer 2

The y coordinates of the vertex and the focus are the same (-3)
So the focal axis must be parallel to the x axis.
The standar form of the ecuation of the parabola with focal axis parallel to the x axis and vertex (h,k) is
(y-k)^2 = 4p(x-h)

Where |p| is the distance between the focus and the vertex

Here the vertex is (1,-3) and the focus is (-2,-3), so the distance between them is 1-(-2=3
And since the focus is on the left of the vertex p =-3

So the ecuation is
(y+3)^2 = -12(x-1)

Answer 3

Thanks!