Write the equation of the parabola with focus at (0,6) and directrix y = -6.?

Question

I forget how to lol.

Answer 1

Sice the focus(0,6) is on the y-axis, the parabola takesthe form x^2=2py , where 2p is the distance between the focus and the directrix. So p= 6 -(-6) =12 and 2p = 24.Thus the equation is x^2 = 24y.

Answer 2

Correction on fcas80's work:
the focus is (0,6) & directrix is y=-6.
the vertex is (0,0).

The equation is (y-k)=(1/{4p})(x-h)^2 where (h,k) is vertex and p is the directed distance from the vertex to the focus. (If the parabola is curving up or down.)

In this case, p = 6. Thus y=(1/24)x^2.

Edit: yeah, wrong formula

Answer 3

dist from focus to directrix = 2p = 12, p = 6.

4*6*(y-6) = (x-0)^2

24(y-6) = x^2

Answer 4

Use distance equation:

(x - 0)^2 + (y - 6)^2 = (x - (-6))^2 + (y - y)^2
x^2 + y^2 - 12y + 36 = x^2 + 12x + 36

y^2 - 12y = 12x
x = (y^2 - 12y) / 12

Answer 5

just use the formula of y=mx +c
where m is gradient and c=6 all you have to do is substitue those two and you'll get the equation
how to calculate a gradient:
http://www.teacherschoice.com.au/Maths_Library/Gradient/gradient_-_origin_to_fixed_point.htm