Conic Sections Question 190
Question: The equation of an ellipse whose focus (-1, 1), whose directrix is $ x-y+3=0 $ and whose eccentricity is $ \frac{1}{2} $ , is given by
[MP PET 1993]
Options:
A) $ 7x^{2}+2xy+7y^{2}+10x-10y+7=0 $
B) $ 7x^{2}-2xy+7y^{2}-10x+10y+7=0 $
C) $ 7x^{2}-2xy+7y^{2}-10x-10y-7=0 $
D) $ 7x^{2}-2xy+7y^{2}+10x+10y-7=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Let any point on it be (x, y), then $ \frac{\sqrt{{{(x+1)}^{2}}}+\sqrt{{{(y-1)}^{2}}}}{| \frac{x-y+3}{\sqrt{2}} |}=\frac{1}{2} $
Squaring and simplifying, we get $ 7x^{2}+2xy+7y^{2}+10x-10y+7=0 $ .
BETA
