Parabolas Graphing Parabolas

Question

Find an equation for the parabola that has its vertex at the origin and has a focus at the point .  Answer should be exact...no rounding.

Answer 1

Since the focus is to the right of the vertex, the y variable will be squared in the equation:

(y-k)^2 = 4p(x-h) where (h,k) is the vertex and p is the distance from the vertex to the focus.

If you plug in what you know:

(y-0)^2 = 4(6.38) (x-0)

y^2 = 25.52x

Sometimes these equations are solved to get the unsquared variable by itself:

x = 1/25.53 y^2