The line, $ lx + my + n = 0$  will cut the ellipse $\frac{{{x^2}}}{{{a^2}}}$ $+$ $\frac{{{y^2}}}{{{b^2}}}$ $= 1 $ in points whose eccentric angles differ by $\pi /2$  if :

If end points of latus rectum of an ellipse are vertices of a square, then eccentricity of ellipse will be -

Let the eccentricity of an ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, a>b$, be $\frac{1}{4}$. If this ellipse passes through the point $\left(-4 \sqrt{\frac{2}{5}}, 3\right)$, then $a^{2}+b^{2}$ is equal to

The equation of normal at the point $(0, 3)$ of the ellipse $9{x^2} + 5{y^2} = 45$ is

Let $A,B$ and $C$ are three points on ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$where line joing $A \,\,\&\,\, C$ is parallel to the $x-$axis and $B$ is end point of minor axis whose ordinate is positive then maximum area of $\Delta ABC,$ is-

A tangent to the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ intersect the co-ordinate axes at $A$ and $B,$ then locus of circumcentre of triangle $AOB$ (where $O$ is origin) is