The locus of mid points of parts in between axes and tangents of ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ will be
$\frac{{{a^2}}}{{{x^2}}} + \frac{{{b^2}}}{{{y^2}}} = 1$
$\frac{{{a^2}}}{{{x^2}}} + \frac{{{b^2}}}{{{y^2}}} = 2$
$\frac{{{a^2}}}{{{x^2}}} + \frac{{{b^2}}}{{{y^2}}} = 3$
$\frac{{{a^2}}}{{{x^2}}} + \frac{{{b^2}}}{{{y^2}}} = 4$
Find the equation for the ellipse that satisfies the given conditions : Vertices $(\pm 5,\,0),$ foci $(\pm 4,\,0)$
If the foci and vertices of an ellipse be $( \pm 1,\;0)$ and $( \pm 2,\;0)$, then the minor axis of the ellipse is
An ellipse and a hyperbola have the same centre origin, the same foci and the minor-axis of the one is the same as the conjugate axis of the other. If $ e_1, e_2 $ be their eccentricities respectively, then $e_1^{ - 2} + e_2^{ - 2}$ equals
If tangents are drawn to the ellipse $x^2 + 2y^2 = 2$ at all points on the ellipse other than its four vertices than the mid points of the tangents intercepted between the coordinate axes lie on the curve
If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is