For an ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ with vertices $A$ and $ A', $ tangent drawn at the point $P$ in the first quadrant meets the $y-$axis in $Q $ and the chord $ A'P$ meets the $y-$axis in $M.$ If $ 'O' $ is the origin then $OQ^2 - MQ^2$ equals to
$9$
$13$
$4$
$5$
The centre of the ellipse $4{x^2} + 9{y^2} - 16x - 54y + 61 = 0$ is
If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity $e$ of the ellipse satisfies
Find the equation of the ellipse, whose length of the major axis is $20$ and foci are $(0,\,\pm 5)$
The equation of the ellipse whose centre is $(2, -3)$, one of the foci is $(3, -3)$ and the corresponding vertex is $(4, -3)$ is
Let $P$ is any point on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ . $S_1$ and $S_2$ its foci then maximum area of $\Delta PS_1S_2$ is (in square units)