Question

Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2.

 

Answer 1

The focus of the parabola is (0, 2) and directrix y = - 2.

Since the directrix is y = -2, the standard form of parabola equation is (x - h)^2 = 4p (y - k).

Find the value of h, k and p as follows :

The equation of directrix  y = k - p = - 2 ⇒ k - p = - 2 ------> (1).

Focus = (h, k + p) = (0, 2) ⇒ h = 0 and k + p = 2       ------> (2).

Solve equation 1 and 2, to obtain k = 0 and p = 2.

The standard form of parabola equation is (x - 0)^2 = 4(2) (y - 0) ⇒ x² = 8y.