Expert: Steve Holleran - 12/18/2007

Question
find the focus and directrix for the parabola with the given equation

x^2 = 36y

answers

1. focus;(9,0); y = 9
2. focus;(0,-9); x= -9
3. focus;(0,9); y = -9
4. focus, (9,0); x = 9

Answer
Hi Chyjuan,

The form you want to use is

            y = (1/4p) x^2  where p is the distance from the vertex to the focus and the directrix.

Solving for y:    y = (1/36) x^2  

 so 4p = 36 and p = 9.  Since this is a vertical parabola, with vertex at (0,0) and opening upward , the focus is 9 units up from (0,0) at (0,9) and the equation for the directrix is the horizontal line 9 units below the origin, so it would be y = -9.

Hope this helps
Steve