Find the equation of the parabola that has vertex at 0 0 and

Find the equation of the parabola that has vertex at (0, 0) and Focus at (0, -3). Write down the equation of its Directrix.

Solution

Vertex=(0,0)

Focus(0,-3)

Focus(h,k +(1/4a))

Here h=0,k=0

Therefore 1/4a=-3

a=-1/12

Directrix,y=k-(1/4a) =0-(-3)=3

Equation is y=(-1/12)x^2