Conic Sections Question 18
Question: The equation of the parabola with focus (a, b) and directrix $ \frac{x}{a}+\frac{y}{b}=1 $ is given by
[MP PET 1997]
Options:
A) $ {{(ax-by)}^{2}}-2a^{3}x-2b^{3}y+a^{4}+a^{2}b^{2}+b^{4}=0 $
B) $ {{(ax+by)}^{2}}-2a^{3}x-2b^{3}y-a^{4}+a^{2}b^{2}-b^{4}=0 $
C) $ {{(ax-by)}^{2}}+a^{4}+b^{4}-2a^{3}x=0 $
D) $ {{(ax-by)}^{2}}-2a^{3}x=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
$ {{(x-a)}^{2}}+{{(y-b)}^{2}}={{( \frac{bx+ay-ab}{\sqrt{a^{2}+b^{2}}} )}^{2}} $
On solving we get $ {{(ax-by)}^{2}}-2a^{3}x-2b^{3}y+a^{4}+a^{2}b^{2}+b^{4}=0 $ .
BETA
