The length of the axes of the conic $9{x^2} + 4{y^2} - 6x + 4y + 1 = 0$, are
$\frac{1}{2},\;9$
$3,\;\frac{2}{5}$
$1,\;\frac{2}{3}$
$3, \;2$
In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is $10$ and one of the foci is at $(0, 5\sqrt 3 )$, then the length of its latus rectum is
Eccentricity of the ellipse $9{x^2} + 25{y^2} = 225$ is
Find the equation for the ellipse that satisfies the given conditions: Vertices $(\pm 6,\,0),$ foci $(\pm 4,\,0)$
From the point$ C(0,\lambda )$ two tangents are drawn to ellipse $x^2\ +\ 2y^2\ = 4$ cutting major axis at $A$ and $B$. If area of $\Delta$ $ABC$ is minimum, then value of $\lambda$ is-
Let $L$ be a common tangent line to the curves $4 x^{2}+9 y^{2}=36$ and $(2 x)^{2}+(2 y)^{2}=31$. Then the square of the slope of the line $L$ is ..... .