Circle And System Of Circles Question 224
Question: The line $ x\cos \alpha +y\sin \alpha =p $ will be a tangent to the circle $ x^{2}+y^{2}-2ax\cos \alpha -2ay\sin \alpha =0 $ , if $ p= $
Options:
A) 0 or a
B) 0
C) $ 2a $
D) $ 0 $ or $ 2a $
Show Answer
Answer:
Correct Answer: D
Solution:
$ x\cos \alpha +y\sin \alpha -p=0 $ is a tangent, if perpendicular from centre on it is equal to radius of the circle. Here centre is $ (a\cos \alpha ,\ a\sin \alpha ) $ and radius is a. \ $ | \frac{a{{\cos }^{2}}\alpha +a{{\sin }^{2}}\alpha -p}{\sqrt{1}} |=a $ i.e. $ |a-p|\ =a\Rightarrow p=0 $ or $ p=2a $ .
BETA
