Question

What is the equation of a parabola with (−2, 4) as its focus and y = 6 as its directrix?

Answer 1

We're given focus =(−2, 4) and directrix Y = 6 We start with this equation:
(x- h)^2 = 4p * (y -k)

The "x" value of the focus = the "x" value of the directrix = -2 (which also = "h")
The "y" value (or "k") lies between the focus "y" value and the directrix "y" value k = (4 + 6 / 2) = 5
p = one half the distance from directrix to focus = .5 * (6 -4) = 1
Now we enter these numbers into:(x- h)^2 = 4p * (y -k)(x --2)^2 = 4*1 * (y -5)(x +2)^2 = 4y -20x^2 + 4 x + 4 = 4y - 204y = x^2 + 4 x + 24 y = x^2/4 + x + 6
Source:http://www.1728.org/quadr4.htm