Eccentricity of the conic $16{x^2} + 7{y^2} = 112$ is
$3\over \sqrt 7 $
$7\over{16}$
$3\over4$
$4\over3$
The length of the latus rectum of the ellipse $\frac{{{x^2}}}{{36}} + \frac{{{y^2}}}{{49}} = 1$
The angle of intersection of ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ and circle ${x^2} + {y^2} = ab$, is
A focus of an ellipse is at the origin. The directrix is the line $x = 4$ and the eccentricity is $ \frac{1}{2}$ . Then the length of the semi-major axis is
The radius of the circle having its centre at $(0, 3)$ and passing through the foci of the ellipse $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{9} = 1$, is
The sum of focal distances of any point on the ellipse with major and minor axes as $2a$ and $2b$ respectively, is equal to