Conic Sections Question 179
Question: The line $ x\cos \alpha +y\sin \alpha =p $ will be a tangent to the conic $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $ , if
[Roorkee 1978]
Options:
A) $ p^{2}=a^{2}{{\sin }^{2}}\alpha +b^{2}{{\cos }^{2}}\alpha $
B) $ p^{2}=a^{2}+b^{2} $
C) $ p^{2}=b^{2}{{\sin }^{2}}\alpha +a^{2}{{\cos }^{2}}\alpha $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ y=-x\cot \alpha +\frac{p}{\sin \alpha } $ is tangent to $ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, $ if $ \frac{p}{\sin \alpha }=\pm \sqrt{b^{2}+a^{2}{{\cot }^{2}}\alpha } $ or $ p^{2}=b^{2}{{\sin }^{2}}\alpha +a^{2}{{\cos }^{2}}\alpha $ .
BETA
