The eccentricity of an ellipse in which distance between their focii is 10 and that of focus and corresponding directrix is 15 is

Question

The eccentricity of an ellipse in which distance between their focii is 10 and that of focus and corresponding directrix is 15 is (A) (1/3) (B) (1/2) (C) (1/4) (D) (1/√2)

Tardigrade Admin · Accepted Answer

2 a e=10 (a/e)-a e=15 a e=5 (5/e2)-5=15 ⇒ (5/e2)=20 ⇒ e=(1/2)

Q. The eccentricity of an ellipse in which distance between their focii is 10 and that of focus and corresponding directrix is 15 is

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{2}$

$2 a e = 10 \frac{a}{e} - a e = 15$
$a e = 5 \frac{5}{e ^{2}} - 5 = 15 \Rightarrow \frac{5}{e ^{2}} = 20 \Rightarrow e = \frac{1}{2}$

Q. The eccentricity of an ellipse in which distance between their focii is 10 and that of focus and corresponding directrix is 15 is

31​

21​

41​

2​1​

2ae=10ea​−ae=15 ae=5e25​−5=15⇒e25​=20⇒e=21​

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{2}$

$2 a e = 10 \frac{a}{e} - a e = 15$
$a e = 5 \frac{5}{e ^{2}} - 5 = 15 \Rightarrow \frac{5}{e ^{2}} = 20 \Rightarrow e = \frac{1}{2}$