Let $P(2,2)$ be a point on an ellipse whose foci are $(5,2)$ and $(2,6)$, then eccentricity of ellipse is
$\frac{2}{3}$
$\frac{5}{7}$
$\frac{1}{3}$
$\frac{3}{4}$
A tangent having slope of $-\frac{4}{3}$ to the ellipse $\frac{{{x^2}}}{{18}}$ + $\frac{{{y^2}}}{{32}}$ $= 1$ intersects the major and minor axes in points $A$ and $ B$ respectively. If $C$ is the centre of the ellipse then the area of the triangle $ ABC$ is : .............. $\mathrm{sq. \,units}$
Which one of the following is the common tangent to the ellipses, $\frac{{{x^2}}}{{{a^2} + {b^2}}} + \frac{{{y^2}}}{{{b^2}}}$ $=1\&$ $ \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{a^2} + {b^2}}}$ $=1$
The acute angle between the pair of tangents drawn to the ellipse $2 x^{2}+3 y^{2}=5$ from the point $(1,3)$ is.
The eccentricity of an ellipse whose centre is at the origin is $\frac{1}{2}$ . If one of its directices is $x = - 4$ then the equation of the normal to it at $\left( {1,\frac{3}{2}} \right)$ is