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 $2$
For the ellipse $3{x^2} + 4{y^2} = 12$, the length of latus rectum is
A common tangent to $9x^2 + 16y^2 = 144 ; y^2 - x + 4 = 0 \,\,\&\,\, x^2 + y^2 - 12x + 32 = 0$ is :
The smallest possible positive slope of a line whose $y$-intercept is $5$ and which has a common point with the ellipse $9 x^2+16 y^2=144$ is
If the centre, one of the foci and semi-major axis of an ellipse be $(0, 0), (0, 3)$ and $5$ then its equation is
A tangent to the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ intersect the co-ordinate axes at $A$ and $B,$ then locus of circumcentre of triangle $AOB$ (where $O$ is origin) is