Mathematics · 2023
JEE Main · 31 January 2023, Shift 2 · Q74
Let H be the hyperbola, whose foci are (1 ± √ 2, 0) and eccentricity is √ 2. Then the length of its latus rectum is ____.
Let H be the hyperbola, whose foci are $\displaystyle (1 \pm \sqrt{2}, 0)$ and eccentricity is $\displaystyle \sqrt{2}$. Then the length of its latus rectum is $\displaystyle \_\_\_\_$.
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle 2$
More from Hyperbola
- Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2a and 2b, respectively, and one focus and the corresponding…2025
- If A and B are the points of intersection of the circle x^2+y^2-8 x=0 and the hyperbola x^2/9-y^2/4=1 and a point P moves on the line 2 x-3 y+4=0,…2025
- Let x^2/(a^2)+y^2/(b^2)=1, a>b be an ellipse, whose eccentricity is 1/(√2) and the length of the latusrectum is √14. Then the square of the…2024
- Let H_1: x^2/(a^2)-y^2/(b^2)=1 and H_2:-x^2/(A^2)+y^2/(B^2)=1 be two hyperbolas having length of latus rectums 15 √2 and 12 √5 respectively. Let…2025
- Let the ellipse E: x^2/144+y^2/169=1 and the hyperbola H: x^2/16-y^2/(λ^2)=-1 have the same foci. If e and L respectively denote the eccentricity and…2026
- The length of the latus rectum and directrices of a hyperbola with eccentricity e are 9 and x= ± 4/(√3), respectively. Let the line y-√3 x+√3=0 touch…2024
- Let the foci and length of the latus rectum of an ellipse x^2/a^2+y^2/b^2=1, a>b be ( ± 5,0) and √50, respectively. Then, the square of the…2024
- Let the foci of a hyperbola H coincide with the foci of the ellipse E: ((x-1)^2)/100+((y-1)^2)/75=1 and the eccentricity of the hyperbola H be the…2024
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.