If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be 1 / 2, then length of the minor axis is

Question

If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be 1 / 2, then length of the minor axis is (A) 3 (B) 4 √2 (C) 6 (D) None of these

Tardigrade Admin · Accepted Answer

Given that, (a/e)-a e=8 Also,⇒ a=(8 e/1-e2)=(8.4/2(3))=(16/3) ∴ b=(16/3) √(1-(1/4))=(16/3) (√3/2)=(8 √3/3) e=(1/2) Hence, the length of minor axis is (16 √3/3).

Q. If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be $1/2$ , then length of the minor axis is

3

$42$

6

None of these

Given that, $\frac{a}{e} - a e = 8$
Also, $\Rightarrow a = \frac{8 e}{1 - e ^{2}} = \frac{8.4}{2 ( 3 )} = \frac{16}{3}$
$∴ b = \frac{16}{3} (1 - \frac{1}{4}) = \frac{16}{3} \frac{3}{2} = \frac{8 3}{3}$
$e = \frac{1}{2}$
Hence, the length of minor axis is $\frac{16 3}{3}$ .

Q. If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be 1/2, then length of the minor axis is

3

42​

6

None of these

Given that, ea​−ae=8 Also,⇒a=1−e28e​=2(3)8.4​=316​ ∴b=316​(1−41​)​=316​23​​=383​​ e=21​ Hence, the length of minor axis is 3163​​.

Q. If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be $1/2$ , then length of the minor axis is

$42$

Given that, $\frac{a}{e} - a e = 8$
Also, $\Rightarrow a = \frac{8 e}{1 - e ^{2}} = \frac{8.4}{2 ( 3 )} = \frac{16}{3}$
$∴ b = \frac{16}{3} (1 - \frac{1}{4}) = \frac{16}{3} \frac{3}{2} = \frac{8 3}{3}$
$e = \frac{1}{2}$
Hence, the length of minor axis is $\frac{16 3}{3}$ .