1.) (3,5),y=1 [][][][[][[[][][] 2.) (4,-4),y=-6?

Question

Writ an equation of a parabola with the given focus and directrix.

Answer 1

Generally, let us have a parabola with focus (m,n) and directrix y=k.
Such a parabola is opened upwards when n>k and the vertex of the parabola is (m, [n+k]/2).
Latus rectum of the parabola is 4a=2(n-k).
The equation of the parabola is (x-m)² = 2(n-k)(y-[n+k]2)

1.)
(x-3)² = 8(y-3)

2.)
(x-4)² = 4(y+5)

Se also http://mathworld.wolfram.com/Parabola.html

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