# \(Squeeze \) Ellipse and Calculus \(\Longrightarrow Ellipsulus \)

**Calculus**Level 5

(a>b).such that the chord \(AK_{r} \) makes an angle of \(\theta=\frac{r\pi}{2n} \) with the positive x axis.

\[\displaystyle{lim_{n\rightarrow\infty}(\frac{1}{n}(\sum_{r=1}^{n}(AK_{r})^{(lim_{n\rightarrow\infty}\sum_{k=1}^{n}(\frac{k}{n^{2}+n+2k}))^{-c}}))=\frac{S}{d} }\]

S is the area of the ellipse

M and M' are the feet of perpendiculars from the foci S and S' to the tangents at any point P on the ellipse . If \(SM=2S'M'\) \(S'P=2\pi \) d is the length of SP

find the value of *\(2c\)*