Find the equation of a parabola with focal point $(-8, -2)$ and directrix $y -2 x + 9 = 0$ > Find the equation of a parabola with focal point $(-8, -2)$ and directrix $y -2 x + 9 = 0$ The equation I got was : $(y+3)^2=-17(x+2)$ but it seems to be wrong. Please help.

> By the defintion of parabola, distance of point $P(x,y)$ from focus and directrix are equal

$$\Rightarrow \cfrac{|y-2x+9|}{\sqrt{5}} = \sqrt{(x+8)^2 + (y+2)^2} $$ On squaring and multiplying both sides by $5$, $$ y^2 + 4x^2 + 81 - 4xy - 36x + 18y = 5x^2 + 320 + 80x + 5y^2 + 20 + 20y$$ $$\Rightarrow x^2 + 4y^2 + 259 + 4xy + 116x + 2y =0$$