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^2 =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 (a) the foci of ellipse are (+-1, 0) (b) equation of ellipse is x^2+ 2y^2 =2 (c) the foci of ellipse are (+-sqrt 2, 0) (d) equation of ellipse is (x^2 +y^2 =4)

The eccentricity of the ellipse x^(2) + 2y^(2) =6 is

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 the ellipse (x^2)/25+(y^2)/9=1 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

In the ellipse (x^(2))/(6)+(y^(2))/(8)=1 , the value of eccentricity is

If e_1 is the eccentricity of the ellipse x^2/16+y^2/25=1 and e_2 is the eccentricity of the hyperbola passing through the foci of the ellipse and e_1 e_2=1 , then equation of the hyperbola is

Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse 9x^2+4y^2=36 .

Find the center, foci, the length of the axes, and the eccentricity of the ellipse 2x^2+3y^2-4x-12 y+13=0