Consider the ellipse `E_1, x^2/a^2+y^2/b^2=1,(a>b)`. An ellipse `E_2` passes through the extremities of the major axis of `E_1` and has its foci at the ends of its minor axis.Consider the following property:Sum of focal distances of any point on an ellipse is equal to its major axis. Equation of `E_2` is

Consider the ellipse E_(1),(x^(2))/(a^(2))+(y^(2))/(b^(2))=1,(a>b). An ellipse E_(2) passes through the extremities of the major axis of E_(1) and has its foci at the ends of its minor axis.Consider the following on an ellipse is equal to its major axis. Equation of E_(2) is

If the latusrectum of an ellipse is half of its major axis then e is

In an ellipse, its foci and the ends of its major axis are equally spaced. If the length of its semi-minor is 2sqrt(2), them the length of its semi-major axis is

Consider an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a gt b) . A hyperbola has its vertices at the extremities of minor axis of the ellipse and the length of major axis of the ellipse is equal to the distance between the foci of hyperbola. Let e_(1) and e_(2) be the eccentricities of ellipse and hyperbola, respectively. Also, let A_(1) be the area of the quadrilateral fored by joining all the foci and A_(2) be the area of the quadrilateral formed by all the directries. The relation between e_(1) and e_(2) is given by

If E_1:x^2/a^2+y^2/b^2=1 , agtb . E_2 is an ellipse which touches E_1 at the ends of major axis of E_1 and end of major axis of E_1 are the focii of E_2 and the eccentricity of both the ellipse are equal then find e

A series of concentric ellipse E_1,E_2,E_3,…,E_n is constructed as follows: Ellipse E_n touches the extremities of the major axis of E_(n-1) and have its focii at the extremities of the minor axis of E_(n-1) If equation of ellipse E_1 is x^(2)/9+y^(2)/16=1 , then equation pf ellipse E_3 is

A series of concentric ellipse E_1,E_2,E_3,…,E_n is constructed as follows: Ellipse E_n touches the extremities of the major axis of E_(n-1) and have its focii at the extremities of the minor axis of E_(n-1) If equation of ellipse E_1 is x^(2)/9+y^(2)/16=1 , then equation pf ellipse E_3 is