Find the equation of tangents to the ellipse $$9x^{2}+16y^{2}=144$$ which passes through the point $$(2, 3)$$.

Show that the line $$15x-8y+44=0$$ touches the ellipse given by $$25x^{2}+4y^{2}-100x-24y+36=0$$. Find the point of contact.

$$C: x^{2}+y^{2}=9$$, $$\displaystyle E: \frac{x^{2}}{9}+\frac{y^{2}}{4}=1$$, $$L: y=2x$$

lf $$\pi+\theta$$ is the eccentric angle of a point on the ellipse $$16x^{2}+25y^{2}=400$$ then the corresponding point on the auxiliary circle is 

The equation of the polar of the focus of the ellipse $$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$$ is