Circle And System Of Circles Question 9
Question: The gradient of the tangent line at the point $ (a\cos \alpha ,a\sin \alpha ) $ to the circle $ x^{2}+y^{2}=a^{2} $ , is
Options:
A) $ \tan \alpha $
B) $ \tan (\pi -\alpha ) $
C) $ \cot \alpha $
D) $ -\cot \alpha $
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Answer:
Correct Answer: D
Solution:
Equation of a tangent at $ (a\cos \alpha ,\ a\sin \alpha ) $ to the circle $ x^{2}+y^{2}=a^{2} $ is $ ax\cos \alpha +ay\sin \alpha =a^{2} $ .
Hence its gradient is $ -\frac{a\cos \alpha }{a\sin \alpha }=-\cot \alpha $ .
BETA
