Conic Sections Question 398
Question: If the latus rectum of an hyperbola be 8 and eccentricity be $ 3/\sqrt{5} $ , then the equation of the hyperbola is
Options:
A) $ 4x^{2}-5y^{2}=100 $
B) $ 5x^{2}-4y^{2}=100 $
C) $ 4x^{2}+5y^{2}=100 $
D) $ 5x^{2}+4y^{2}=100 $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{2b^{2}}{a}=8 $ and $ \frac{3}{\sqrt{5}}=\sqrt{1+\frac{b^{2}}{a^{2}}} $ or $ \frac{4}{5}=\frac{b^{2}}{a^{2}} $
therefore $ a=5 $ , $ b=2\sqrt{5} $ .
Hence the required equation of hyperbola is $ \frac{x^{2}}{25}-\frac{y^{2}}{20}=1 $
therefore $ 4x^{2}-5y^{2}=100 $ .
BETA
