Question

S and S are the focii of the ellipse `x^2/a^2 + y^2/b^2 - 1` whose one of the ends of the minor axis is the point B If ∠SBS' = 90°, then the eccentricity of the ellipse is

Options

• `1/2`

• `1/sqrt(2)`

• `1/(2sqrt(2))`

• `1/(2sqrt(3))`

Answer 1

`1/sqrt(2)`

Explanation:

∴ ∠SBS' = 90° ⇒ BS² + BS'² = SS'²

∴ `(sqrt(a^2e^2 + b^2))^2 + (sqrt(a^2e^2 + b^2))^2 = (2ae)^2`

⇒ `e^2 = b^2/a^2`

Also, `e^2 = 1 - b^2/a^2 = 1 - e^2`

⇒ `2e^2 = 1`

⇒ `e = 1/sqrt(2)`