write an equation of a parabola with vertex at the origin and the given focus

Question

focus at (0,2)

Answer 1

Write an equation of a parabola with vertex at the origin and the given focus, focus at (0,2)

 

The focus form of a parabola is:

 

4p(y-k) = (x-h)²

 

Where p is the distance from the vertex to the focus (both points lie on the axis of symmetry), and (h.k) is the position of the vertex.  In your case, the vertex lies at (0,0) so the equation becomes:

 

4py = x²

 

The focus lies at (0,2) so it is 2 units away from the vertex (which is at (0,0)).  So p=2:

 

4(2)y = x²

 

8y = x²

 

y = (1/8)x²