If a focal chord of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ meets its minor axis at the point $(0,3)$,then the perpendicular distance from the centre of the ellipse to this focal chord is

For which of the following curves is the line $x+\sqrt{3} y=2 \sqrt{3}$ a tangent at the point $\left(\frac{3 \sqrt{3}}{2}, \frac{1}{2}\right)$?

The latus rectum of an ellipse is $10$ and the minor axis is equal to the distance between the foci. The equation of the ellipse is

$A$ particle is travelling in a clockwise direction on the ellipse $\frac{x^2}{100} + \frac{y^2}{25} = 1$. If the particle leaves the ellipse at the point $(-8, 3)$ and travels along the tangent to the ellipse at that point,then the point where the particle crosses the $Y$-axis is:

$A$ tangent having slope of $-\frac{4}{3}$ to the ellipse $\frac{x^2}{18} + \frac{y^2}{32} = 1$ intersects the major and minor axes in points $A$ and $B$ respectively. If $C$ is the centre of the ellipse,then the area of the triangle $ABC$ is: .............. $sq. \,units$

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 :