Let the eccentricity of an ellipse (x²)/(a²)+(y²)/(b²)=1 is reciprocal to that of the hyperbola 2 x²-2 y²=1. If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is _ _ _ _ _ _.

Coordinate Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 6 Apr, Evening shift · Q39

JEE Main 20236 Apr, Evening shiftMathematicsMediumCoordinate Geometry478× since 2002

Let the eccentricity of an ellipse

\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1

is reciprocal to that of the hyperbola

2 x^{2}-2 y^{2}=1

. If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is ___________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2023 · 6 Apr, Evening shift · Q39

JEE Main 20236 Apr, Evening shiftMathematicsMediumCoordinate Geometry478× since 2002

Let the eccentricity of an ellipse

\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1

is reciprocal to that of the hyperbola

2 x^{2}-2 y^{2}=1

. If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is ___________.

Your answerType your answer. Integers and decimals are accepted.