Find-the-equation-of-parabola-whose-focus-1-2-and-directrix-x-2y-3-0-

Question Number 76862 by vishalbhardwaj last updated on 31/Dec/19

Find the equation of parabola

whose focus (- 1, - 2) and directrix

x - 2 y + 3 = 0 ? ?

Answered by mr W last updated on 31/Dec/19

p o i n t P (x, y) o n p a r a b o l a

\sqrt{{(x + 1)}^{2} + {(y + 2)}^{2}} = \frac{x - 2 y + 3}{\sqrt{1^{2} + {(- 2)}^{2}}}

{(x + 1)}^{2} + {(y + 2)}^{2} = \frac{{(x - 2 y + 3)}^{2}}{5}

5 (x^{2} + 2 x + 1) + 5 (y^{2} + 4 y + 4) = x^{2} + 4 y^{2} + 9 + 2 (- 2 x y + 3 x - 6 y)

4 x^{2} + y^{2} + 4 x y + 4 x + 32 y + 16 = 0

Commented by mr W last updated on 31/Dec/19

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