The length of the latus rectum of $16x^2 + 25y^2 = 400$ is

The curves $\frac{x^2}{a^2} + \frac{y^2}{16} = 1$ and $y^3 = 16x$ intersect each other orthogonally,then $a^2 =$

The eccentricity of the ellipse $25x^2 + 16y^2 - 150x - 175 = 0$ is

Let $p$ be the number of all triangles that can be formed by joining the vertices of a regular polygon $P$ of $n$ sides and $q$ be the number of all quadrilaterals that can be formed by joining the vertices of $P$. If $p+q=126$,then the eccentricity of the ellipse $\frac{x^2}{16}+\frac{y^2}{n}=1$ is :

If the minimum area of the triangle formed by a tangent to the ellipse $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{4 a^{2}}=1$ and the coordinate axes is $kab$,then $k$ is equal to ..... .

Find the locus of the midpoint of the portion of the tangent to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ intercepted between the axes.