Find the equation of a parabola with focus (6,0) and vertex at the origin.

Answer 1

The focus form of a parabola is : 4 p(y-k)=(x-h)²

Where p is the distance from the vertex to the focus and (h,k) is the position of vertex where vertex at origin i.e at (0,0)

Then equation 4 p(y-0)=(x-0)²

4 p(y)=(x)²

4py = x²

The focus lie on (6,0) so it is 6 units away from vertex (0,0) so p = 6

Then equation 4 × 6 (0-y)= (x-0)²

24y = x²

or y = 1/24 x²