If the normal at any point $P$ on the ellipse cuts the major and minor axes in $G$ and $g$ respectively and $C$ be the centre of the ellipse, then
${a^2}{(CG)^2} + {b^2}{(Cg)^2} = {({a^2} - {b^2})^2}$
${a^2}{(CG)^2} - {b^2}{(Cg)^2} = {({a^2} - {b^2})^2}$
${a^2}{(CG)^2} - {b^2}{(Cg)^2} = {({a^2} + {b^2})^2}$
None of these
A point on the ellipse, $4x^2 + 9y^2 = 36$, where the normal is parallel to the line, $4x -2y-5 = 0$ , is
An ellipse passes through the point $(-3, 1)$ and its eccentricity is $\sqrt {\frac{2}{5}} $. The equation of the ellipse is
If the distance between a focus and corresponding directrix of an ellipse be $8$ and the eccentricity be $1/2$, then length of the minor axis is
Equation of the ellipse whose axes are the axes of coordinates and which passes through the point $(-3,1) $ and has eccentricity $\sqrt {\frac{2}{5}} $ 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 : .............. $\mathrm{sq. \,units}$