The eccentricity of the ellipse $25{x^2} + 16{y^2} = 100$, is
$\frac{5}{{14}}$
$\frac{4}{5}$
$\frac{3}{5}$
$\frac{2}{5}$
Product of slopes of common tangents to the ellipse $\frac{x^2}{32} + \frac{y^2}{8} = 1$ and parabola $y^2 = 8x$ is -
The eccentricity of ellipse $(x-3)^2 + (y -4)^2 = \frac{y^2}{9} +16 ,$ is -
Locus of the foot of the perpendicular drawn from the centre upon any tangent to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, is
A circle has the same centre as an ellipse and passes through the foci $F_1 \& F_2$ of the ellipse, such that the two curves intersect in $4$ points. Let $'P'$ be any one of their point of intersection. If the major axis of the ellipse is $17 $ and the area of the triangle $PF_1F_2$ is $30$, then the distance between the foci is :
If the length of the major axis of an ellipse is three times the length of its minor axis, then its eccentricity is