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Area of an Ellipse

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Calculate the area, circumference, axis ratio, and distance from the center to a focus of an ellipse using its semi-major and semi-minor axes.
Semi-major axis a
Semi-minor axis b
b≦a
Area S 
Circumference L 
Axis ratio c (b/a) 
Distance from center to focus f 
\(\normalsize Ellipse\\ (1)\ area:\hspace{85px} S=ab\pi,\hspace{20px} b\le a\\ (2)\ circumference:\\ \hspace{20px} L=4aE(k),\hspace{20px} k=\sqrt{1-({\large\frac{b}{a}})^2}\\ \hspace{20px} E(k):\ 2nd\ complete\ elliptic\ integral\\(3)\ ellipticity:\hspace{40px} c={\large\frac{b}{a}}\\ (4)\ linear\ eccentricity :\ f=\sqrt{a^2-b^2}\\\)

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