Question

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 coordinates axes, then

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

Answer 1

The correct option is B the foci of ellipse are $(\pm 1,0)$

If two concentric conics intersect orthogonally then they must be confocal, so ellipse and hyperbola will be confocal
$\Rightarrow (\pm ae,0)=(\pm 1,0)$
[foci of ellipse are\) $(\pm 1,0)$ ]