The equation of the parabola whose directrix | vedclass

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(B) Let $P(x, y)$ be any point on the parabola. By the definition of a parabola,the distance from $P$ to the focus $S(-8, -2)$ is equal to the perpend

Vedclass · Accepted Answer

$x^2 + 4y^2 + 4xy + 116x + 2y + 259 = 0$

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(B) Let $P(x, y)$ be any point on the parabola. By the definition of a parabola,the distance from $P$ to the focus $S(-8, -2)$ is equal to the perpendicular distance from $P$ to the directrix $2x - y - 9 = 0$.$PS = \frac{|2x - y - 9|}{\sqrt{2^2 + (-1)^2}}$$\sqrt{(x + 8)^2 + (y + 2)^2} = \frac{|2x - y - 9|}{\sqrt{5}}$Squaring both sides:$(x + 8)^2 + (y + 2)^2 = \frac{(2x - y - 9)^2}{5}$$5(x^2 + 16x + 64 + y^2 + 4y + 4) = 4x^2 + y^2 + 81 - 4xy - 36x + 18y$$5x^2 + 5y^2 + 80x + 20y + 340 = 4x^2 + y^2 - 4xy - 36x + 18y + 81$$x^2 + 4y^2 + 4xy + 116x + 2y + 259 = 0$.

The equation of the parabola whose directrix is $y = 2x - 9$ and focus is $(-8, -2)$ is:

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