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
$0$
$1$
$2$
more than $2$
The angle between the pair of tangents drawn from the point $(1, 2)$ to the ellipse $3{x^2} + 2{y^2} = 5$ is
Find the equation for the ellipse that satisfies the given conditions : Vertices $(\pm 5,\,0),$ foci $(\pm 4,\,0)$
On the ellipse $4{x^2} + 9{y^2} = 1$, the points at which the tangents are parallel to the line $8x = 9y$ are
If $PQ$ is a double ordinate of hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ such that $OPQ$ is an equilateral triangle, $O$ being the centre of the hyperbola. Then the eccentricity $e$ of the hyperbola satisfies