### Ellipse

goals
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