parabolas

Question

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, 9)

Answer 1

Parabola vertex at origin and focus at (0,9)

The x coordinate of the vertex and focus is same, so the required parabola is vertical parabola.

Vertex of parabola (h, k) = (0, 0)

h = 0, k = 0

Vertical parabola focus is (h, k + p) = (0, 9)

k + p = 9

Substitute k = 0.

p = 9

Standard form of vertical parabola

Substitute (h, k) and p values in standardform.

The parabola equation is .