Conic Sections Question 462
Question: If transverse and conjugate axes of a hyperbola are equal, then its eccentricity is
[MP PET 2003]
Options:
A) $ \sqrt{3} $
B) $ \sqrt{2} $
C) $ 1/\sqrt{2} $
D) 2
Show Answer
Answer:
Correct Answer: B
Solution:
Hyperbola is $ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 $ . Here, transverse and conjugate axis of a hyperbola is equal. i.e., $ a=b $
$ \therefore x^{2}-y^{2}=a^{2} $ ; which is a rectangular hyperbola.
Hence, eccentricity $ e=\sqrt{1+\frac{b^{2}}{a^{2}}}=\sqrt{2} $ .
BETA
