The eccentricity of the ellipse $9{x^2} + 5{y^2} - 30y = 0$, is
$1\over3$
$2\over3$
$3\over4$
None of these
The centre of an ellipse is $C$ and $PN$ is any ordinate and $A$, $A’$ are the end points of major axis, then the value of $\frac{{P{N^2}}}{{AN\;.\;A'N}}$ is
The foci of the ellipse $25{(x + 1)^2} + 9{(y + 2)^2} = 225$ are at
The line $12 x \,\cos \theta+5 y \,\sin \theta=60$ is tangent to which of the following curves?
If the length of the latus rectum of an ellipse is $4\,units$ and the distance between a focus and its nearest vertex on the major axis is $\frac {3}{2}\,units$ , then its eccentricity is?
The line passing through the extremity $A$ of the major axis and extremity $B$ of the minor axis of the ellipse $x^2+9 y^2=9$ meets its auxiliary circle at the point $M$. Then the area of the triangle with vertices at $A, M$ and the origin $O$ is