1. Tardigrade
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  3. Mathematics
  4. If the distances of foci and vertex of hyperbola from the centre are c and a respectively, then I. Eccentricity is always less than 1. II. Foci are at a distance of a ℓ from the centre.

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Q. If the distances of foci and vertex of hyperbola from the centre are $c$ and $a$ respectively, then
I. Eccentricity is always less than 1.
II. Foci are at a distance of $a \ell$ from the centre.

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Solution:

Since, $c \geq a$, the eccentricity is never less than one. In terms of the eccentricity the foci are at a distance of ae from the centre.