1. Tardigrade
  2. Question
  3. Mathematics
  4. Let the foci of the hyperbola (x2/A2)-(y2/B2)=1 be the vertices of the ellipse (x2/a2)+(y2/b2)=1 and the foci of the ellipse be the vertices of the hyperbola. Let the eccentricities of the ellipse and hyperbola be e1 and e2 respectively. Given b=1 and e2=2. The length of the latus-rectum of the hyperbola is equal to

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Q. Let the foci of the hyperbola $\frac{x^2}{A^2}-\frac{y^2}{B^2}=1$ be the vertices of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and the foci of the ellipse be the vertices of the hyperbola. Let the eccentricities of the ellipse and hyperbola be $e_1$ and $e_2$ respectively. Given $b=1$ and $e_2=2$.
The length of the latus-rectum of the hyperbola is equal to

Conic Sections

Solution:

$l$ (latus rectum of hyperbola) $=\frac{2 B ^2}{ A }=2 \sqrt{3}$.