The locus of the point of intersection of the tangent drawn at the points on $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$ whose eccentric angles differ by 2$\mathrm{\theta }$ is $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}={\mathrm{k}}^2\text{ then }\mathrm{k}=$

$$\begin{gathered} Let the points on ellipse be P ( a \cos \theta , b \sin \theta ) and \\ Q ( a \cos ( 2\theta + \theta ) , b \sin ( 2\theta + \theta ) ) = (a\cos 3\theta ,b\sin 3\theta ) \\ Equation of \tan gent at point P: \frac{x }{a} \cos \theta + \frac{y}{b}\sin \theta = 1 \end{gathered}$$