Find an equation of the parabola?

Question

Find an equation of the parabola that has a focus at (6,15) and a vertex at (6, 6) :


y =?


i thought it was (y-6)^2=36(x-6) but it not... so please help

Answer 1

Find an equation of the parabola that has a focus at (6,15) and a vertex at (6, 6).

So focus is on a line parallel to y-axis (ie axis is parallel to y-axis)

Parabola with vertex at (h, k) is of form:

X² = 4aY where X = x - h, Y = y - k and a is the focal length

In this case vertex is (6, 6) and focal length = 9 (axis is parallel to y-axis)

So equation is given by
(x - 6)² = (4 * 9)(y - 6)
ie (x - 6)² = 36(y - 6)
So x² - 12x + 36 = 36(y - 6)
So y - 6 = x²/36 - x/3 + 1
ie y = x²/36 - x/3 + 7

Answer 2

What is the definition of the focus? see: http://en.wikipedia.org/wiki/Parabola