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.

Question

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. (A) Both I and II are true (B) Only I is true (C) Only II is true (D) Both I and II are false

Tardigrade Admin · Accepted Answer

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

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 $a ℓ$ from the centre.

Both I and II are true

Only I is true

Only II is true

Both I and II are false

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.

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 aℓ from the centre.