Question

Find the equation of the parabola with its vertex at (h,k). Vertex: (-2.1) Focus: (-5,1)

I know I put it into (y-k)^2=4(p)(x-h) so (y-1)^2=4(p)(x+2).
How do I find the value of p?

Answer 1

F(-5,1), V(-2,1)

VF = -5-(-2) = -3 = 1/4a
1/4a = -3
4a = -1/3
a = -1/12 = p.

X = a(y-k)^2 + h
X = (-1/12)(y-1)^2 - 2. Vertex Form.