Latus rectum of ellipse $4{x^2} + 9{y^2} - 8x - 36y + 4 = 0$ is

The eccentricity of the ellipse ${\left( {\frac{{x - 3}}{y}} \right)^2} + {\left( {1 - \frac{4}{y}} \right)^2} = \frac{1}{9}$ is

The eccentricity of the ellipse $ (x - 3)^2 + (y - 4)^2 =$ $\frac{{{y^2}}}{9}\,$  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-

$P$ is a variable point on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ with $AA'$ as the major axis. Then the maximum value of the area of $\Delta APA'$ is

Let $S$ and $S\,'$ be the foci of an ellipse and $B$ be any one of the extremities of its minor axis. If $\Delta S\,'BS$ is a right angled triangle with right angle at $B$ and area $(\Delta S\,'BS) = 8\,sq.$ units, then the length of a latus rectum of the ellipse is