The lengths of major and minor axis of an ellipse are $10$ and $8$ respectively and its major axis along the $y$ - axis. The equation of the ellipse referred to its centre as origin is
$\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1$
$\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{25}} = 1$
$\frac{{{x^2}}}{{100}} + \frac{{{y^2}}}{{64}} = 1$
$\frac{{{x^2}}}{{64}} + \frac{{{y^2}}}{{100}} = 1$
The eccentricity of the ellipse ${\left( {\frac{{x - 3}}{y}} \right)^2} + {\left( {1 - \frac{4}{y}} \right)^2} = \frac{1}{9}$ is
The equation of the ellipse whose vertices are $( \pm 5,\;0)$ and foci are $( \pm 4,\;0)$ is
Find the equation for the ellipse that satisfies the given conditions: Foci $(\pm 3,\,0),\,\, a=4$
Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse, $\frac{x^{2}}{4}+\frac{y^{2}}{2}=1$ from any of its foci?
The eccentricity of the ellipse $\frac{{{{(x - 1)}^2}}}{9} + \frac{{{{(y + 1)}^2}}}{{25}} = 1$ is