A series of concentric ellipses `E_1,E_2, E_3..., E_n` are drawn such that E touches the extremities of the major axis of `E_(n-1)`, and the foci of `E_n` coincide with the extremities of minor axis of `E_(n-1)` If the eccentricity of the ellipses is independent of n, then the value of the eccentricity, 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 eccentricity of ellipse E_n is e_n , then the locus of (e_(n)^(2),e_(n-1)^(2)) 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

Find the equation of the ellipse the extremities of whose minor axis are (3, 1) and (3, 5) and whose eccentricity is 1/2 .

Find the equation of the ellipse in the following case: eccentricity e=1/2 and semi major axis =4 .

Find the equation of the ellipse in the following case: eccentricity e=1/2 and major axis =12

S and T are the foci of the ellipse x^2/a^2+y^2/b^2 = 1 and B is an end of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is e then find value of 4e

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

The foci of an ellipse are (-2,4) and (2,1). The point (1,(23)/(6)) is an extremity of the minor axis. What is the value of the eccentricity?

If the line joining foci subtends an angle of 90^(@) at an extremity of minor axis, then the eccentricity e is

Consider an ellipse x^2/a^2+y^2/b^2=1 Let a hyperbola is having its vertices at the extremities of minor axis of an ellipse and length of major axis of an ellipse is equal to the distance between the foci of hyperbola. Let e_1 and e_2 be the eccentricities of an ellipse and hyperbola respectively. Again let A be the area of the quadrilateral formed by joining all the foci and A, be the area of the quadrilateral formed by all the directrices. The relation between e_1 and e_2 is given by