Three different catenary curves through the same points. Each curve corresponds to different values of horizontal force <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{H}\,}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>T</mi><mrow class="MJX-TeXAtom-ORD"><mi>H</mi></mrow></msub><mspace width="thinmathspace"></mspace></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle T_{H}\,}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/107ae60ef7365ad75a91777dcaa7acbb1e802a21" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:3.436ex; height:2.509ex;" alt="{\displaystyle T_{H}\,}"></span>, being <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a={\frac {T_{H}}{wH}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>a</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msub><mi>T</mi><mrow class="MJX-TeXAtom-ORD"><mi>H</mi></mrow></msub><mrow><mi>w</mi><mi>H</mi></mrow></mfrac></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle a={\frac {T_{H}}{wH}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e83dc7693aae2698fd7242bac8e15a7c1cbf0b2" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:8.892ex; height:5.176ex;" alt="{\displaystyle a={\frac {T_{H}}{wH}}}"></span>, and w the weight per unit of length
<a href="//commons.wikimedia.org/wiki/User:%D0%94.%D0%98%D0%BB%D1%8C%D0%B8%D0%BD" title="User:Д.Ильин">Д.Ильин</a>: vectorization
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