Question

How can I find the equation of a parabola with vertex (4,3), focal length of 1/2 and opens down?

Answer 1

Since it opens down I know it is (x-4)^2=-...(y-3) but I don't know what to do with the focal length

Answer 2

Since it opens down it is of the form x^2=4py

Answer 3

Wait focal length is p right? So 2

Answer 4

p = 1/2 and 4p = 2
So:
x^2=2y
Now apply the shift for the vertex:
(x-4)^2=2(y-3)

Answer 5

It opens down, so wouldn't it be (x-4)^2=-2(y-3)?

Answer 6

No. -2y-3 Without the parentheses

Answer 7

ty

Answer 8

yw