jee-advanced 2009 Q25

jee-advanced · India · paper2 Conic sections Equation Determination from Geometric Conditions

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
(A) Equation of ellipse is $x^{2}+2y^{2}=2$
(B) The foci of ellipse are $(\pm1,0)$
(C) Equation of ellipse is $x^{2}+2y^{2}=4$
(D) The foci of ellipse are $(\pm\sqrt{2},0)$

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\\
(A) Equation of ellipse is $x^{2}+2y^{2}=2$\\
(B) The foci of ellipse are $(\pm1,0)$\\
(C) Equation of ellipse is $x^{2}+2y^{2}=4$\\
(D) The foci of ellipse are $(\pm\sqrt{2},0)$

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