If tangents are drawn from point $P(3\ sin\theta + 4\ cos\theta , 3\ cos\theta\ -\ 4\ sin\theta)$ , $\theta = \frac {\pi}{8}$ to the ellipse $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{9} = 1$ then angle between the tangents is

The length of the latus rectum of the ellipse $\frac{{{x^2}}}{{36}} + \frac{{{y^2}}}{{49}} = 1$

The equation of an ellipse whose focus $(-1, 1)$, whose directrix is $x - y + 3 = 0$ and whose eccentricity is $\frac{1}{2}$, is given by

If the distance between the foci of an ellipse is $6$ and the distance between its directrices is $12$, then the length of its latus rectum is

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis $(0,\, \pm \sqrt{5})$ ends of minor axis $(±1,\,0)$

The length of the chord of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$, whose mid point is $\left(1, \frac{2}{5}\right)$, is equal to: