Mathematics · 2023
JEE Main · 6 April 2023, Shift 2 · Q27
Let the eccentricity of an ellipse x^2/a^2+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…
Let the eccentricity of an ellipse $\displaystyle \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is reciprocal to that of the hyperbola $\displaystyle 2 x^2-2 y^2=1$. If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is $\displaystyle \_\_\_\_$.
Official answer
From NTA’s final answer key for this paper.
2
More from Ellipse
- Let the line y-x=1 intersect the ellipse x^2/2+y^2/1=1 at the points A and B. Then the angle made by the line segment AB at the center of the ellipse…2026
- If α x+β y=109 is the equation of the chord of the ellipse x^2/9+y^2/4=1, whose mid point is (5/2, 1/2), then α+β is equal to:2025
- Let an ellipse with centre (1,0) and latus rectum of length 1/2 have its major axis along x -axis. If its minor axis subtends an angle 60^° at the…2023
- Let (h, k) lie on the circle C: x^2+y^2=4 and the point (2 h+1,3 k+2) lie on an ellipse with eccentricity e. Then the value of 5/e^2 is equal to ____.2026
- The equation of the chord, of the ellipse x^2/25+y^2/16=1, whose mid-point is (3,1) is:2025
- The length of the latus-rectum of the ellipse, whose foci are (2,5) and (2,-3) and eccentricity is 4/5, is2025
- The length of the chord of the ellipse x^2/4+y^2/2=1, whose mid-point is (1, 1/2), is:2025
- If the points of intersection of two distinct conics x^2+y^2=4 b and x^2/16+y^2/b^2=1 lie on the curve y^2=3 x^2, then 3 √3 times the area of the…2024
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.