Conic Sections Question 458
Question: A tangent to a hyperbola $ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 $ intercepts a length of unity from each of the co-ordinate axes, then the point (a, b) lies on the rectangular hyperbola
Options:
A) $ x^{2}-y^{2}=2 $
B) $ x^{2}-y^{2}=1 $
C) $ x^{2}-y^{2}=-1 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Tangent at $ (a\sec \theta ,b\tan \theta ) $ is, $ \frac{x}{(a/\sec \theta )}-\frac{y}{(b/\tan \theta )}=1 $ or $ \frac{a}{\sec \theta }=1,\frac{b}{\tan \theta }=1 $
therefore $ a=\sec \theta $ , $ b=\tan \theta $ or $ (a,b) $ lies on $ x^{2}-y^{2}=1 $ .
BETA
