Q. The equation of parabola whose focus is $(5,3)$ and directrix is $3x - 4y + 1 = 0$, is
A) ${(4x + 3y)}^{2} - 256x - 142y + 849 = 0$
B) ${(4x - 3y)}^{2} - 256x - 142y + 849 = 0$
C) ${(3x + 4y)}^{2} - 142x - 256y + 849 = 0$
D) ${(3x - 4y)}^{2} - 256x - 142y + 849 = 0$
Explanation
(a)
By definition of parabola ${PM}^{2} = PS^{2}$
$\left\lbrack \frac{3x - 4y + 1}{\sqrt{3^{2} + ( - 4)^{2}}} \right\rbrack^{2} = {(x - 5)}^{2} + {(y - 3)}^{2}$
[image:11_image46.emf]
$\Rightarrow 9x^{2} + 16y^{2} + 1^{2} - 24xy - 8y + 6x$
$= 25(x^{2} + 25 - 10x + y^{2} + 9 - 6y)$
$\Rightarrow 16x^{2} + 9y^{2} - 256x - 142y + 24xy + 849 = 0$
$\Rightarrow {(4x + 3y)}^{2} - 256x - 142y + 849 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.