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
${\tan ^{ - 1}}\left( {\frac{{a - b}}{{ab}}} \right)$
${\tan ^{ - 1}}\left( {\frac{{a + b}}{{ab}}} \right)$
${\tan ^{ - 1}}\left( {\frac{{a + b}}{{\sqrt {ab} }}} \right)$
${\tan ^{ - 1}}\left( {\frac{{a - b}}{{\sqrt {ab} }}} \right)$
If the minimum area of the triangle formed by a tangent to the ellipse $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{4 a^{2}}=1$ and the co-ordinate axis is $kab,$ then $\mathrm{k}$ is equal to ..... .
Find the coordinates of the foci, the rertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $16 x^{2}+y^{2}=16$
If $P \equiv (x,\;y)$, ${F_1} \equiv (3,\;0)$, ${F_2} \equiv ( - 3,\;0)$ and $16{x^2} + 25{y^2} = 400$, then $P{F_1} + P{F_2}$ equals
In the ellipse, minor axis is $8$ and eccentricity is $\frac{{\sqrt 5 }}{3}$. Then major axis is
The distance between the focii of the ellipse $(3x - 9)^2 + 9y^2 =(\sqrt 2 x + y +1)^2$ is-