Find the standard form of the equation of the parabola with a focus at (0, -10) and a directrix at y = 10.

Answer 1

The parabola directrix at y = 10 and focus at (0, 10)

The vertical parabola directrix equation is y = k - p

Therfore, the required parabola is horizontal.

Standard form of vertcal parabola is

Where Center (h, k ),focus is (h , k+p ) and directrix is y  = k - p

Directrix y = k - p

k - p = 10 -----> (1)

Focus (h, k+p) = (0, -10)

k + p = -10 ----> (2)

and k = 0

Add the equations (1) & (2).

2k = 0

k = 0

Substitute h value in equation (2).

0+ p = -10

p = -10

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

substitute h, k , p values in standard form.

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

x^2 =4(-10)(y)

x^2=-40y

Parabola equation is ​x^2=-40y