what-the-equation-of-parabola-whose-focus-F-3-4-and-directrix-is-3x-4y-5-0-

Question Number 112664 by bemath last updated on 09/Sep/20

what the equation of parabola

whose focus F (- 3, 4) and directrix

is 3 x - 4 y + 5 = 0 ?

Commented by bemath last updated on 09/Sep/20

Answered by bobhans last updated on 09/Sep/20

(⧫) \sqrt{{(x + 3)}^{2} + {(y - 4)}^{2}} = ∣ \frac{3 x - 4 y + 5}{5} ∣

squaring \Rightarrow {(x - 3)}^{2} + {(y - 4)}^{2} = \frac{{(3 x - 4 y + 5)}^{2}}{25}

\Rightarrow 25 (x^{2} + y^{2} - 6 x - 8 y + 25) = {9 x}^{2} + {16 y}^{2} + 25 - 24 xy + 30 x - 40 y

\Rightarrow {16 x}^{2} + {9 y}^{2} + 24 xy - 150 x - 160 y + 600 = 0

Facebook Tweet Pin