Area of a hyperbolic arch Calculator

Calculates the area and arc of a hyperbolic arch given two parameters and a section line.

 $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
parameters a
b
section line x
 ≧a

area of arch S
eccentricity e
length of arc L
 $\normal Hyperbolic\ Arch\\(1)\ area: \hspace{20} y={\large\frac{b}{a}}\sqrt{x^2-a^2}\\\hspace{50} S=ab\cosh^{\tiny -1}{\large\frac{x}{a}}\\\vspace{10}\\(2)\ eccentricity : \hspace{10} e={\large\frac{\sqrt{a^2+b^2}}{a}}\\(3)\ hyperbolic\ arch:\\\hspace{50} k={\large\frac{1}{e}},\hspace{5} z=\sqrt{\large\frac{x^2-a^2}{x^2-(ka)^2}}\\\hspace{50} L={\large\frac{1}{k}}\left{a(1-k^2)F(z,k)-aE(z,k)+xz\right}\\\vspace{10}\\$

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