An ellipse, with foci at $(0, 2)$ and $(0, -2)$ and minor axis of length $4$, passes through which of the following points?
$(2, \sqrt 2 )$
$(2, 2\sqrt 2 )$
$(1, 2\sqrt 2 )$
$( \sqrt 2, 2 )$
The eccentricity of the ellipse $4{x^2} + 9{y^2} + 8x + 36y + 4 = 0$ is
The distance between the foci of an ellipse is 16 and eccentricity is $\frac{1}{2}$. Length of the major axis of the ellipse is
If the normal at the point $P(\theta )$ to the ellipse $\frac{{{x^2}}}{{14}} + \frac{{{y^2}}}{5} = 1$ intersects it again at the point $Q(2\theta )$, then $\cos \theta $ is equal to
The number of values of $c$ such that the straight line $y = 4x + c$ touches the curve $\frac{{{x^2}}}{4} + {y^2} = 1$ is
Find the equation for the ellipse that satisfies the given conditions: $b=3,\,\, c=4,$ centre at the origin; foci on the $x$ axis.