Conic Sections Question 212
Question: The equation of the conic with focus at (1, -1), directrix along $ x-y+1=0 $ and with eccentricity $ \sqrt{2} $ is
[EAMCET 1994]
Options:
A) $ x^{2}-y^{2}=1 $
B) $ xy=1 $
C) $ 2xy-4x+4y+1=0 $
D) $ 2xy+4x-4y-1=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
Let P (x, y) be any point on the conic. Then $ \sqrt{{{(x-1)}^{2}}+{{(y+1)}^{2}}}=\sqrt{2}( \frac{x-y+1}{\sqrt{2}} ) $ , [Using $ SP=e.PM] $
$ \Rightarrow 2xy-4x+4y+1=0 $ .
BETA
