The equations of the tangents to the ellipse $9x^2 + 16y^2 = 144$ which pass through the point $(2, 3)$ are

The normal at a point $P$ on the ellipse $x^2 + 4y^2 = 16$ meets the $x$-axis at $Q$. If $M$ is the midpoint of the line segment $PQ$,then the locus of $M$ intersects the latus rectum of the given ellipse at which points?

If the chords of contact of tangents drawn from two points $(x_1, y_1)$ and $(x_2, y_2)$ to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ are at right angles,then $\frac{x_1 x_2}{y_1 y_2} = \dots$

If $P$ is a point on $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ with foci $S$ and $S^{\prime}$,then the maximum area of $\triangle S P S^{\prime}$ is

Find the equation of the ellipse whose latus rectum is $10$ and the length of the minor axis is equal to the distance between the foci.

Let $S$ and $S'$ be the foci of the ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$ and $P$ be a variable point on the ellipse. The maximum area of the triangle $PSS'$ is ............. square units.