Find the equation of a parabola with focus F(0, -3) and directrix y = 3.

Question

anonymous · Answer

@mml

anonymous · Answer

haha you love tagging me dont you ?

tkhunny · Answer

Do you know what it looks like?

(y-k) = p(x-h)^2
or
(x-h) = p(y-k)^2

You must know this or you can't do it very well.

anonymous · Answer

Yes! :P

tkhunny · Answer

Alternatively, the Definition of the Parabola can be useful.

Locus of points equidistant from a given point (focus) and a given line (directrix).

Given all points, (x,y)

The distance from (0,-3) is $\sqrt{(x-0)^{2} + (y+3)^{3}} = \sqrt{x^{2} + y^{2} + 6x + 9}$

The distance from y = 3 is $|y-3|$

Those two expressions must be equal.

$\sqrt{x^{2} + y^{2} + 6x + 9} = |y-3|$

$x^{2} + y^{2} + 6x + 9 = y^{2} - 6y + 9$

You're almost done.