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Ellipse question

2009 · Shift 2 · Q36

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PYQ Library
JEE Advanced
Mathematics
Ellipse
2009 · Shift 2 · Q36

Ellipse question

2009 · Shift 2 · Q36

JEE AdvancedMathematicsEllipseMultiple correct+4 / −2

An ellipse intersects the hyperbola

2{x^2} - 2{y^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 ${x^2} + 2{y^2} = 2$
B
the foci of ellipse are $\left( { \pm 1,0} \right)$
C
equation of ellipse is ${x^2} + 2{y^2} = 4$
D
the foci of ellipse are $\left( { \pm \sqrt 2 ,0} \right)$

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