MATH SOLVE

2 months ago

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

Accepted Solution

A:

The parabola directrix at x = 7 and focus at (-7, 0)The horizontal parabola directrix equation is x = h - pTherfore, 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 - pDirectrix x = h - ph - p = 7 -----> (1)Focus (h + p, k) = (-7, 0)h + p = - 7 ----> (2)and k = 0Add the equations (1) & (2).2h = 0h = 0Substitute h value in equation (2).0 + p = - 7p = - 7Vertex of parabola is (h, k) = (0, 0).substitute h, k , p values in standard form.(y-0)^2 =(4)(-7)xy^2 =-28x