Is there a formula for finding the focus of a vertical parabola?

Question

For instance, the formula for finding the focus of a HORIZONTAL parabola is (h + p , k). What is it for a vertical parabola?

Answer 1

The focus of a vertical parabola works exactly the same way, except it's in the y-direction instead of the x-direction.

That is, the focus of a horizontal parabola is (h, k + p).

(So to find the focus of a vertical parabola, you need to write it in the form y = (1/(4p))(x - h)^2 + k, and solve for p.)

Answer 2

If y= ax^2+bx+c
xF=-b/2a
yF=(4ac-b^2+1)/4a