An ellipse intersects the hyperbola 2x^2...

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)`

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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 (pmsqrt2,0) (d) equation of ellipse is x^2+ 2y^2 =1

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The eccentricity of the ellipse 5x^(2) + 9y^(2) = 1 is _

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An ellipse passes through the point (2,3) and its axes along the coordinate axes, 3x +2y -1 = 0 is a tangent to the ellipse, then the equation of the ellipse is

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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: (a) the equation of the hyperbola is x^2/3-y^2/2=1 (b) a focus of the hyperbola is (2,0) (c) the eccentricity of the hyperbola is sqrt(5/3) (d) the equation of the hyperbola is x^2-3y^2=3

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