What is the equation in standard form of the parabola with a focus at (56,44) and a directrix of y= 34?

1 Answer
Yonas Yohannes
Feb 23, 2016

y = 1/(2(b-k))(x-a)^2 + 1/2 (b+k) where
Point, F(a,b) is focus y = k is the directrix
y = 1/20(x^2-112x+2356)

Explanation:

Without deriving it I claim the equation of a parabola in terms of point of F(a,b) and a Directrix, y = k is given by:
y = 1/(2(b-k))(x-a)^2 + 1/2 (b+k)
In this problem Focus is F(56,44) and Directrix, y = 34
y = 1/(2(44-34))(x-56)^2 + 1/2 (44+34)
y = 1/20(x^2-112x+2356)

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