The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points $(4,-1)$ and $(-2, 2)$ is
$\frac{1}{2}$
$\frac{2}{{\sqrt 5 }}$
$\frac{{\sqrt 3 }}{2}$
$\frac{{\sqrt 3 }}{4}$
The locus of the point of intersection of perpendicular tangents to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, is
Number of common tangents of the ellipse $\frac{{{{\left( {x - 2} \right)}^2}}}{9} + \frac{{{{\left( {y + 2} \right)}^2}}}{4} = 1$ and the circle $x^2 + y^2 -4x + 2y + 4 = 0$ is
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 length of the latus rectum of an ellipse is $\frac{1}{3}$ of the major axis. Its eccentricity is
The radius of the circle having its centre at $(0, 3)$ and passing through the foci of the ellipse $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{9} = 1$, is