Conic Sections Question 38
Question: The equation of parabola whose focus is (5, 3) and directrix is $ 3x-4y+1=0 $ , is
[MP PET 2002]
Options:
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 $
Show Answer
Answer:
Correct Answer: A
Solution:
$ PM^{2}=PS^{2} $
$ \Rightarrow $ $ {{(x-5)}^{2}}+{{(y-3)}^{2}}={{( \frac{3x-4y+1}{\sqrt{9+16}} )}^{2}} $
therefore $ 25(x^{2}+25-10x+y^{2}+9-6x) $
$ =9x^{2}+16y^{2}+1-12xy+6x-8y-12xy $
therefore $ 16x^{2}+9y^{2}-256x-142y+24xy+849=0 $
$ \Rightarrow $ $ {{(4x+3y)}^{2}}-256x-142y+849=0. $
BETA
