Conic Sections Question 240
Question: The eccentricity of an ellipse is 2/3, latus rectum is 5 and centre is (0, 0). The equation of the ellipse is
Options:
A) $ \frac{x^{2}}{81}+\frac{y^{2}}{45}=1 $
B) $ \frac{4x^{2}}{81}+\frac{4y^{2}}{45}=1 $
C) $ \frac{x^{2}}{9}+\frac{y^{2}}{5}=1 $
D) $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ {{( \frac{2}{3} )}^{2}}=1-\frac{b^{2}}{a^{2}} $ and $ \frac{2b^{2}}{a}=5 $
therefore $ a=\frac{81}{4} $ , $ b=\frac{45}{4} $
Hence the equation is $ \frac{4x^{2}}{81}+\frac{4y^{2}}{45}=1 $ .
BETA
