Question

The area of an ellipse is $8\pi$ sq. units and the distance between the focii 4$\sqrt{3}$. Then eccentricity of the ellipse is

• A. sin30⁰
• B. sin45⁰
• C. sin60⁰
• D. sin70⁰

Answer 1

Answer: (C)

sin60⁰

Answer 2

Given πab =8π,

ab = 8, 2a = 4$\sqrt{3}$

ae = 2$\sqrt{3}$

a²e² =12

a² – b² =12

a² - $\frac{64}{a^{2}} = 12$ (let a²= t)

t² – 12t – 64 =0

(t – 16)(t +4) =0

⇒ a² = 16

⇒ a = 4

but ae = $2\sqrt{3}$

∴ e = $\frac{\sqrt{3}}{2}$ = sin 60⁰.