Conic Sections Question 255
Question: The latus rectum of an ellipse is 10 and the minor axis is equal to the distance between the foci. The equation of the ellipse is
Options:
A) $ x^{2}+2y^{2}=100 $
B) $ x^{2}+\sqrt{2}y^{2}=10 $
C) $ x^{2}-2y^{2}=100 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Given $ \frac{2b^{2}}{a}=10 $ and $ 2b=2ae $ Also $ b^{2}=a^{2}(1-e^{2}) $
therefore $ e^{2}=(1-e^{2}) $
therefore $ e=\frac{1}{\sqrt{2}} $
therefore $ b=\frac{a}{\sqrt{2}} $ or $ b=5\sqrt{2} $ , $ a=10 $
Hence equation of ellipse is $ \frac{x^{2}}{{{(10)}^{2}}}+\frac{y^{2}}{{{(5\sqrt{2})}^{2}}}=1 $ i.e., $ x^{2}+2y^{2}=100 $ .
BETA
