The ellipse `x^(2)/a^(2) + y^(2)/b^(2) = 1` and hyperbola `x^(2)/A^(2) - y^(2)/B^(2) = 1` are given to be confocal and length of minor axis is of ellipse is same as the conjugate axis of the hyperbola . If `e_(1)" and " e_(2)` are the eccentricity of ellipse and hyperbola then value of `1/((e_(1))^(2)) + 1/((e_(2))^(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

If e_(1) and e_(2) are the eccentricities of the hyperbola and its conjugate hyperbola respectively then (1)/(e_(1)^(2))+(1)/(e_(2)^(2)) is equal to

An ellipse and a hyperbola are confocal (have the same focus) and the conjugate axis of the hyperbola is equal to the minor axis of the ellipse.If e_(1) and e_(2) are the eccentricities of the ellipse and the hyperbola,respectively, then prove that (1)/(e_(1)^(2))+(1)/(e_(2)^(2))=2

If the foci of the ellipse (x^(2))/(25)+(y^(2))/(b^(2))=1 and the hyperbola (x^(2))/(144)-(y^(2))/(81)=(1)/(25) coincide,then length of semi-minor axis is

If e_(1) and e_(2) are the eccentricities of a hyperbola 3x^(2)-2y^(2)=25 and its conjugate, then

Let e_(1), and e_(2), be the roots of the equation x^(2)-lambda x+2=0 If e_(1) and e_(2), are eccentricities of ellipse and hyperbola then lambda is equal to

If e_(1) , e_(2) " and " e_(3) the eccentricities of a parabola , and ellipse and a hyperbola respectively , then