Let hyperbola `H : x^2-y^2=1` and ellipse `E : x^2/a^2+y^2/b^2=1` and eccentricity of ellipse E is reciprocal of that of hyperbola H . If common tangent of H & E is `y=sqrt(5/2)x+k`, then value of `4(a^2+b^2)` is equal to

An ellipse intersects the hyperbola 2x^(2)-2y^(2)=1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then

An ellipse intersects the hyperbola 2x^2-2y =1 orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then (b) the foci of ellipse are (+-1, 0) (a) equation of ellipse is x^2+ 2y^2 =2 (d) the foci of ellipse are (t 2, 0) (c) equation of ellipse is (x^2 2y)

An elllipse intersects the hyperbola 2x^(2) - 2y^(2) =1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes and the equation of the ellipse is x^(2) + ky^(2) =k then the value of k is ______ .

The eccentricity of the ellipse 9x^2+25y^2=225 is e then the value of 5e is

E_1:x^2/81 +y^2/b^2=1 and E_2: x^2/b^2+y^2/49=1 two ellipses having the same eccentricity if b^2 is equal to

If the hyperbola xy=4 and ellipse (x^(2))/(8)+(y^(2))/(a^(2))=1 have a commone tangent,then

If the eccentricity of the hyperbola conjugate to the hyperbola (x^2)/(4)-(y^2)/(12)=1 is e, then 3e^2 is equal to:

Locus of mid-point of the focal chord of ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with eccentricity e is