If $\frac{{\sqrt 3 }}{a}x + \frac{1}{b}y = 2$ touches the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ then its, eccentric angle $\theta $ is equal to: ................ $^o$
$30$
$45$
$60$
$90$
The equation to the locus of the middle point of the portion of the tangent to the ellipse $\frac{{{x^2}}}{{16}}$$+$ $\frac{{{y^2}}}{9}$ $= 1$ included between the co-ordinate axes is the curve :
In the ellipse, minor axis is $8$ and eccentricity is $\frac{{\sqrt 5 }}{3}$. Then major axis is
The locus of the point of intersection of the perpendicular tangents to the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ is
An ellipse is drawn with major and minor axes of lengths $10 $ and $8$ respectively. Using one focus as centre, a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. The radius of the circle is