Question

Find the focus and directrix of parabola xsquared= 2y

Answer 1

directrix: y = -1/2; focus = (0,1/2)

Explanation:

rewrite in standard form:

2y = x^2

factor 4

4 * (y/2) = x^2

rewrite as

4 * 1/2 ( y - 0 ) = (x - 0 )^2

therefore

(h,k) = (0,0) , p = 1/2

directrix is line || to x-axis, distance - p from the center (0,0) y-coordinate (of the parabola)

y = 0 - p

y = 0 - 1/2

y = -1/2

now for the focus!

the focus is distance p from center (0,0) along y-axis --> (0, 0+p)

therefore

(0,0+1/2)

(0,1/2) is the focus!