Write the equation of the parabola with a vertex at the origin and the focus at (11.5, 0)

Answer 1

The basic equations are:

(x - h)² = 4p (y - k) and (y - k)² = 4p (x - h)

When I sketch the vertex and the focus, this shows that the parabola opens up. This means it would use this version of the equation.

(x - h)² = 4p (y - k)

The vertex is (h,k). Since it says the vertex is at the origin, this would be (0,0) The p value is the distance between the vertex and the origin. In this case, 11.5. Plugging all this in.

(x - 0)² = 4(11.5) (y - 0) Simplify

x² = 46y