Find the equation of the parabola with focus at 0 2 and vert

Find the equation of the parabola with focus at (0, 2) and vertex at (0, 0) Transform the polar equation into rectangular form. r = -4 cos theta

Solution

Focus (0,2) and vertex(0,0)

The parabola have the following form

y=(1/4p)(x-h)²+k

Here vertex (h,k) is (0,0)

focii (h,k+p) which is (0,2)

Therefore p=2

Hence the required equation is

y=(1/8)x² = x²/8