Conic Sections Question 24
Question: Let S and S’ be two foci of the ellipse $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $ if a circle described on SS’ as diameter intersects the ellipse at real and distinct points, then the eccentricity e of the ellipse satisfies
Options:
A) $ e=1/\sqrt{2} $
B) $ e\in (1/\sqrt{2,}1) $
C) $ e\in (0,1/\sqrt{2,}) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] The radius of circle having SS’ as diameter is r=ae. If it cuts an ellipse, then r>b or ae>b or $ e^{2}>\frac{b^{2}}{a^{2}} $ or $ e^{2}>1-e^{2} $ or $ e^{2}>\frac{1}{2} $ or $ e>\frac{1}{\sqrt{2}} $ or $ e\in ( \frac{1}{\sqrt{2}},1 ) $
BETA
