Question

let $S$,$S^1$ be the foci of an ellipse. If $\angle BS{S}^1$ = $\theta$,where B is any point on the ellipse. Then its eccentricity is

• A. tan $\theta$
• B. sin $\theta$
• C. cos $\theta$
• D. cot $\theta$

Answer 1

The correct option is C

cos $\theta$

tan $\theta$ = $\frac{b}{ae}$

SB = $\sqrt{b^2+a^2{e}^2}$ = a

cos $\theta$ $\frac{ae}{a}$ = e

e = cos $\theta$