Circle And System Of Circles Question 312
Question: If the line y $ \cos \alpha =x\sin \alpha +a\cos \alpha $ be a tangent to the circle $ x^{2}+y^{2}=a^{2} $ , then
Options:
A) $ {{\sin }^{2}}\alpha =1 $
B) $ {{\cos }^{2}}\alpha =1 $
C) $ {{\sin }^{2}}\alpha =a^{2} $
D) $ {{\cos }^{2}}\alpha =a^{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
The tangent is y $ \cos \alpha =x\sin \alpha +a\cos \alpha $
$ \Rightarrow y=x\tan \alpha +a $
It is a tangent to the circle $ x^{2}+y^{2}=a^{2} $ , if $ a^{2}=a^{2}(1+{{\tan }^{2}}\alpha )\Rightarrow {{\sec }^{2}}\alpha =1\Rightarrow {{\cos }^{2}}\alpha =1 $ .
BETA
