Mathematics - Application of Derivative Question with Solution | TestHub

We have $y^2=4a\left(x+a\sin \frac{x}{a}\right)$ ...(i) Differentiating w.r. $\mathrm{tx}$, $2y\frac{dy}{dx}=4a\left[1+\cos \frac{x}{a}\right]$ Since, the tangent is parallel to $x-$ axis, $\frac{dy}{dx}=0$ This gives $4a\left(1+\cos \frac{x}{a}\right)=0\Rightarrow \cos \frac{x}{a}=-1\Rightarrow \sin \frac{x}{a}=0$ $\therefore$ From (i) $y^2=4a(x+0)\Rightarrow y^2=4ax$, which is the required locus.