The equation of the tangent to the circle, given by $x=5 \cos heta, y=5 \sin heta$ at the point $ heta=\frac{\pi}{3}$ on it, is

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The equation of the tangent to the circle, given by $x=5 \cos 	heta, y=5 \sin 	heta$ at the point $	heta=\frac{\pi}{3}$ on it, is

Aicharya · Accepted Answer

The equation of the tangent to the circle $x^2+y^2=\mathrm{a}^2$ at $\mathrm{P}(\theta)$ is $x \cos \theta+y \sin \theta=\mathrm{a}$
Here, $a=5, \theta=\frac{\pi}{3}$ $\therefore \quad$ The equation of the tangent is $\begin{aligned} & x \cos \frac{\pi}{3}+y \sin \frac{\pi}{3}=5 \\ & \Rightarrow x\left(\frac{1}{2}\right)+y\left(\frac{\sqrt{3}}{2}\right)=5 \\ & \Rightarrow x+y \sqrt{3}=10 \end{aligned}$

The equation of the tangent to the circle, given by $x=5 \cos \theta, y=5 \sin \theta$ at the point…

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