Conic Sections Question 61
Question: If any tangent to the ellipse $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $ cuts off intercepts of length h and k on the axes, then $ \frac{a^{2}}{h^{2}}+\frac{b^{2}}{k^{2}}= $
Options:
A) 0
B) 1
C) -1
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
The tangent at $ (a\cos \theta ,b\sin \theta ) $ to the ellipse is $ \frac{(a\cos \theta )x}{a^{2}}+\frac{(b\sin \theta )y}{b^{2}}=1 $ or $ \frac{x}{(a/\cos \theta )}+\frac{y}{(b/\sin \theta )}=1 $
$ \therefore $ Intercepts are, $ h=\frac{a}{\cos \theta },k=\frac{b}{\sin \theta } $
therefore $ \frac{a^{2}}{h^{2}}+\frac{b^{2}}{k^{2}}=1 $ .
BETA
