An equation of a parabola is given x 2y2 Find the focus dir

An equation of a parabola is given. x = -2y^2 Find the focus, directrix, and focal diameter of the parabola. focus (x, y) = (_____) directrix ______ focal diameter _______

Solution

x = -2y^2

y^2 = 4(-1/8)x

p = 1/8

focus : (-1/8 , 0 )

directrix : x = 0 - (- 1/8)

x = 1/8

Focal diameter = 4|p| = 4*1/8 = 1/2