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10-1.Circle and System of Circles
medium
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
A
$\tan \alpha $
B
$\tan (\pi - \alpha )$
C
$\cot \alpha $
D
$ - \cot \alpha $
Solution
(d) 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 $.
Standard 11
Mathematics
