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
$\frac{{{b^2}}}{{{a^2}}}$
$\frac{{{a^2}}}{{{b^2}}}$
${a^2} + {b^2}$
$1$
If $A = [(x,\,y):{x^2} + {y^2} = 25]$ and $B = [(x,\,y):{x^2} + 9{y^2} = 144]$, then $A \cap B$ contains
If the tangent to the parabola $y^2 = x$ at a point $\left( {\alpha ,\beta } \right)\,,\,\left( {\beta > 0} \right)$ is also a tangent to the ellipse, $x^2 + 2y^2 = 1$, then $a$ is equal to
If $m$ is the slope of a common tangent to the curves $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$ and $x^{2}+y^{2}=12$, then $12\; m ^{2}$ is equal to
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
An ellipse having foci at $(3, 1)$ and $(1, 1) $ passes through the point $(1, 3),$ then its eccentricity is