write the standard equation for the parabola with the given characteristics. vertex(-3,2); focus(-3,-3)?

Question

this is dealing with conics.

Answer 1

The vertex and focus are in a vertical line so the parabola opens vertically.

The directed distance from the vertex to the focus is p.

p = -3 - 2 = -5.

The equation of a vertical parabols with vertex (h,k) is:

4p(y - k) = (x - h)²
4(-5)(y - -3) = (x - -3)²
-20(y + 3) = (x + 3)²

This is the vertex form. If you want the standard form multiply it out.

y + 3 = (-1/20)(x² + 6x + 9)
y + 3 = -(1/20)x² - (3/10)x - 9/20
y = -(1/20)x² - (3/10)x - 69/20

Answer 2

I believe it would be (x+3)squared= -12(y-2)squared