The product of the lengths of perpendiculars from the foci on any tangent to the ellipse $3x^2 + 5y^2 = 1$, is
$\frac{1}{5}$
$\frac{3}{5}$
$\frac{5}{3}$
$5$
The locus of the middle point of the intercept of the tangents drawn from an external point to the ellipse ${x^2} + 2{y^2} = 2$ between the co-ordinates axes, is
An ellipse inscribed in a semi-circle touches the circular arc at two distinct points and also touches the bounding diameter. Its major axis is parallel to the bounding diameter. When the ellipse has the maximum possible area, its eccentricity is
The eccentricity of an ellipse is $2/3$, latus rectum is $5$ and centre is $(0, 0)$. The equation of the ellipse is
The line $y=x+1$ meets the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{2}=1$ at two points $P$ and $Q$. If $r$ is the radius of the circle with $PQ$ as diameter then $(3 r )^{2}$ is equal to
The eccentricity of the ellipse $9{x^2} + 5{y^2} - 30y = 0$, is