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 ______ .

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)

The eccentricity of an ellipse with centre at the orgin and axes along the coordinate axes , is 1/2 if one of the directrices is x=4, the equation of the ellipse is

The eccentricity of an ellipse is 1/2 and the distance between its foci is 4 units. If the major and minor axes of the ellipse are respectively along the x and y axes, find the equation of the ellipse

The eccentricity of an ellipse is 1/2 and the distance between its foci is 4 units. If the major and minor axes of the ellipse are respectively along the x and y axes, find the equation of the ellipse.

The eccentricity of the ellipse ax ^(2) + by ^(2) + 2 fx + 2gy + c =0 if axis of ellipse parallel to x -

Let the eccentricity of the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 be reciprocal to that of the ellipse x^(2) + 4y^(2) = 4 . If the hyperbola passes through a focus of the ellipse, then

If the eccentricity of the hyperbola x^(2)-y^(2)sec^(2)theta=4 is sqrt3 times the eccentricity of the ellipse x^(2)sec^(2)theta+y^(2)=16 , then the value of theta equals

Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 be the reciprocal to that of the ellipse x^(2)+4y^(2)=4 . If the hyperbola passes through a focus of the ellipse, then the equation of the hyperbola, is