If radii of director circles of `x^2/a^2+y^2/b^2=1 and x^2/a^2-y^2/b^2=1` are `2r and r` respectively, let `e_E and e_H` are the eccentricities of ellipse and hyperbola respectively, then

If radii of director circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are in the ratio 1:3 and 4e_(1)^(2)-e_(2)^(2)=lambda , where e_1 and e_2 are the eccetricities of ellipse and hyperbola respectively, then the value of lambda is

If radii of director circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are in the ratio 1:3 and 4e_(1)^(2)-e_(2)^(2)=lambda , where e_1 and e_2 are the eccetricities of ellipse and hyperbola respectively, then the value of lambda is

Let the major axis of a standard ellipse equals the transverse axis of a standard hyperbola and their director circles have radius equal to 2R and R respectively. If e_(1) and e_(2) , are the eccentricities of the ellipse and hyperbola then the correct relation is

Let the major axis of a standard ellipse equals the transverse axis of a standard hyperbola and their director circles have radius equal to 2R and R respectively. If e_(1) and e_(2) , are the eccentricities of the ellipse and hyperbola then the correct relation is

Let the major axis ofa standard ellipse equals the transverse axis of a standard hyperbola and their director circles have radius equal to 2R and R respectively. If e, and e, are the eccentricities ofthe ellipse and hyperbola then the correct relation is (a) 4e_1^2-e_2^2=6 (b) e_1^2-4e_2^2=2 (c) 4e_2^2-e_1^2=6 (d) 2e_1^2-e_2^2=4

The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the hyperbola (x^(2))/(A^(2))-(y^(2))/(B^(2))=1 are given to be confocal and length of mirror axis of the ellipse is same as the conjugate axis of the hyperbola. If e_1 and e_2 represents the eccentricities of ellipse and hyperbola respectively, then the value of e_(1)^(-2)+e_(1)^(-2) is

The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the hyperbola (x^(2))/(A^(2))-(y^(2))/(B^(2))=1 are given to be confocal and length of mirror axis of the ellipse is same as the conjugate axis of the hyperbola. If e_1 and e_2 represents the eccentricities of ellipse and hyperbola respectively, then the value of e_(1)^(-2)+e_(1)^(-2) is

The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the hyperbola (x^(2))/(A^(2))-(y^(2))/(B^(2))=1 are given to be confocal and length of mirror axis of the ellipse is same as the conjugate axis of the hyperbola. If e_1 and e_2 represents the eccentricities of ellipse and hyperbola respectively, then the value of e_(1)^(-2)+e_(1)^(-2) is