Circle-And-System-Of-Circles Question 377
The line $ 3x-2y=k $ meets the circle $ x^{2}+y^{2}=4r^{2} $ at only one point, if $ k^{2} $ = 32r²
[Karnataka CET 2003]
Options:
A) $ p=a\cos \alpha $
B) $ p=a\tan \alpha $
C) $ p^{2}=a^{2} $
D) $ p\sin \alpha =a $
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Answer:
Correct Answer: C
Solution:
According to question length of perpendicular from the centre of circle to the line is equal to the radius of the circle. OM = radius of circle $ | \frac{-p}{\sqrt{{{\cos }^{2}}\alpha +{{\sin }^{2}}\alpha }} |=a $ Þ $ |-p|\ =a\Rightarrow p^{2}=a^{2} $ .
BETA
