Write the standard form equation of the parabola with directrix x=3 and vertex at the origin.

Answer 1

This will be a parabola on its side opening to its left as the vertex is midway between the focus and directrix ( draw a picture) thus the equation will be 4p(x-h)=- (y-k)^2

In this case p= 3 ( the distance from the directrix to the vertex is the same as the distance from the focus to the vertex)

h and k are the coordinates of the vertex which is this case are both 0

so 4p (x-0)=-(y-0)^2

12x= -y^2

x=-(1/12)y^2