Find the standard form of the equation of the parabola with a focus at (-7, 0) and a directrix at x = 7.

Answer 1

The parabola directrix at x = 7 and focus at (-7, 0)

The horizontal parabola directrix equation is x = h - p

Therfore, the required parabola is horizontal.

Standard form of horizontal parabola is

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

Directrix x = h - p

h - p =  7 -----> (1)

Focus (h + p, k) = (-7, 0)

h + p = - 7 ----> (2)

and k = 0

Add the equations (1) & (2).

2h = 0

h = 0

Substitute h value in equation (2).

0 + p = - 7

p = - 7

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

substitute h, k , p values in standard form.

(y-0)^2 =(4)(-7)x

y^2 =-28x

Parabola equation is y^2 =-28x