If the foci and vertices of an ellipse be $( \pm 1,\;0)$ and $( \pm 2,\;0)$, then the minor axis of the ellipse is
$2\sqrt 5 $
$2$
$4$
$2\sqrt 3 $
If the area of the auxiliary circle of the ellipse $\frac{{{x^2}}}{{{a^2}}}\, + \,\frac{{{y^2}}}{{{b^2}}}\, = \,1(a\, > \,b)$ is twice the area of the ellipse, then the eccentricity of the ellipse is
If end points of latus rectum of an ellipse are vertices of a square, then eccentricity of ellipse will be -
The eccentricity of an ellipse whose centre is at the origin is $\frac{1}{2}$ . If one of its directices is $x = - 4$ then the equation of the normal to it at $\left( {1,\frac{3}{2}} \right)$ is
If $x = 9$ is the chord of contact of the hyperbola ${x^2} - {y^2} = 9$, then the equation of the corresponding pair of tangents is
The locus of the point of intersection of mutually perpendicular tangent to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, is