Conic Sections Question 404
Question: The equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13, is
Options:
A) $ 25x^{2}-144y^{2}=900 $
B) $ 144x^{2}-25y^{2}=900 $
C) $ 144x^{2}+25y^{2}=900 $
D) $ 25x^{2}+144y^{2}=900 $
Show Answer
Answer:
Correct Answer: A
Solution:
Conjugate axis is 5 and distance between foci = 13
therefore $ 2b=5 $ and $ 2ae=13 $ . Now, also we know for hyperbola $ b^{2}=a^{2}(e^{2}-1) $
therefore $ \frac{25}{4}=\frac{{{(13)}^{2}}}{4e^{2}}(e^{2}-1) $
therefore $ \frac{25}{4}=\frac{169}{4}-\frac{169}{4e^{2}} $ or $ e^{2}=\frac{169}{144} $
therefore $ e=\frac{13}{12} $
or $ a=6,b=\frac{5}{2} $ or hyperbola is $ \frac{x^{2}}{36}-\frac{y^{2}}{25/4}=1 $
therefore $ 25x^{2}-144y^{2}=900 $ .
BETA
