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

Answer: (D)

$-\cot \alpha$

equation of tangent at point $(x_1,y_1)$ to a circle $x^2+y^2=a^2$ is $x{x}_1+y{y}_1=a^2$
now, $ax\cos \alpha +ay\sin \alpha =a^2$
Therefore, gradient $=-\frac{a\cos \alpha }{a\sin \alpha }=-\cot \alpha$