Question

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

Answer 1

`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)`