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f\left(x\right)=a\cosh\left(\frac{x-x_{0}}{a}\right)+y_{0} \\ f'\left(x\right)=\sinh\left(\frac{x-x_{0}}{a}\right) \\ L=\int\limits_0^{s_1}\sqrt{1+(f'(x))^2}\,\text{d}x = \int\limits_0^{s_1}\cosh\left(\frac{x-x_{0}}{a}\right)\,\text{d}x \\ \phantom{L}= \left.a\sinh\left(\frac{x-x_{0}}{a}\right)\right|_0^{s_1}\\ \phantom{L}= a\left(\sinh\left(\frac{s_1-x_{0}}{a}\right)-\sinh\left(\frac{-x_{0}}{a}\right)\right)\\ \phantom{L}= a\left(f'(s_0)-f'(0)\right)\\ f(0)=h_1=20 \\ h_1=a\cosh\left(\frac{-x_{0}}{a}\right)+y_{0} \\ y_0= h_1-a\cosh\left(\frac{-x_{0}}{a}\right)\\
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