Let the foci of the Ellipse $\dfrac{x^2}{16}+\dfrac{y^2}{7}=1$ and Hyperbola $\dfrac{x^2}{144}-\dfrac{y^2}{\alpha}=\dfrac{1}{25}$ coincide. Then the length of the latus rectum of the Hyperbola is
Step-by-Step Solution
Key Concept: Match foci of ellipse and hyperbola; find $\alpha$; compute latus rectum
Ellipse foci: $(\pm 3,0)$. Hyperbola: $a^2=144/25$, $c=3$, $b^2=9-144/25=81/25$. LR$=2b^2/a=27/10$.
Correct Answer: 2