Hyperbola
Latus Rectum of Hyperbola
nta_pyq_2023_jan
Grade 11
Question:
Let H be the hyperbola, whose foci are $(1 \pm \sqrt{2}, 0)$ and eccentricity is $\sqrt{2}$. Then the length of its latus rectum is ______.
2
3
$\dfrac{5}{2}$
$\dfrac{3}{2}$
Step-by-Step Solution
Key Concept: From $ae = \sqrt{2}$ and $e = \sqrt{2}$, find $a=1$, then $b^2 = a^2(e^2-1)=1$; latus rectum $= 2b^2/a$.
$ae=\sqrt{2}$, $e=\sqrt{2}\Rightarrow a=1$. $b^2=a^2(e^2-1)=1$. Latus rectum $=2b^2/a=2$.
Correct Answer: 1