If the line $y = 2x + c$ be a tangent to the ellipse $\frac{{{x^2}}}{8} + \frac{{{y^2}}}{4} = 1$, then $c = $
$ \pm 4$
$ \pm 6$
$ \pm 1$
$ \pm 8$
Find the equation for the ellipse that satisfies the given conditions: Vertices $(\pm 6,\,0),$ foci $(\pm 4,\,0)$
An ellipse having foci at $(3, 1)$ and $(1, 1) $ passes through the point $(1, 3),$ then its eccentricity is
The line $x\cos \alpha + y\sin \alpha = p$ will be a tangent to the conic $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, if
The equation of the ellipse whose foci are $( \pm 5,\;0)$ and one of its directrix is $5x = 36$, is
In an ellipse, its foci and ends of its major axis are equally spaced. If the length of its semi-minor axis is $2 \sqrt{2}$, then the length of its semi-major axis is