Question

Find the equation of the parabola with focus (3,-4) and directrix 6x-7y+2

Answer 1

Answer:

For any point P(x,y) on the parabola, the distance to the focus F(3, -4) is equal to the perpendicular distance to the Directrix line D, 6x-7y+5=0.

\frac{ {6x - 7y + 5}^2}{(6^2 + 7^2 )} = (x - 3)^2 + (y + 4)^2 \\ \\ 36 x^2 + 49 y^2 + 25 - 84xy - 70y + 60x = 85 x^2 + 85 y^2 - 510x - 2125 + 680y \\ \\ 49 x^2 + 36^2 + 84xy - 570x + 750y - 2150 = 0 \\ \\this \: is \: the \: parabola.