Mathematics - Application of Derivative Question with Solution | TestHub

Length of tangent $=\left|\frac{y_1\sqrt{1+m^2}}{m}\right|$, Length of sub-tangent $=\left|\frac{y_1}{m}\right|$ $\frac{dx}{d\theta }=c(-2\sin \theta +\csc \theta ),\frac{dy}{d\theta }=2c\cos 2\theta$; at $\theta =\frac{\pi }{3}:\frac{dx}{d\theta }=-\frac{c}{\sqrt{3}},\frac{dy}{d\theta }=-c\Rightarrow m=\sqrt{3},y_1=\frac{c\sqrt{3}}{2}$ Sum $=\left|\frac{y_1}{m}\right|+\left|\frac{y_1\sqrt{1+m^2}}{m}\right|=\frac{c}{2}+\frac{c\sqrt{3}/2\times 2}{\sqrt{3}}=\frac{c}{2}+c=\frac{3c}{2}$