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

• A. $\tan (\pi -\alpha )$
• B. $\tan \alpha$
• C. $\cot \alpha$
• D. $-\cot \alpha$

Answer 1

The correct option is D $-\cot \alpha$

$x^2+y^2=a^2$

$\Rightarrow 2x+2y\frac{dy}{dx}=0$

$\Rightarrow \frac{dy}{dx}=\frac{-x}{y}$

$\therefore$ at $(a\cos \alpha ,a\sin \alpha )\Rightarrow$ quadrant is

$\frac{dy}{dx}=-\left(\frac{a\cos \alpha }{a\sin \alpha }\right)$

$=-cot\alpha$