hyperbola

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1: 19.30 Lengths of Plane Curves

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§19.30(ii) Hyperbola

►The arclength $s$ of the hyperbola … ►See Carlson (1977b, Ex. 9.4-1 and (9.4-4)) for arclengths of hyperbolas and ellipses in terms of $R_{-a}$ that differ only in the sign of $b^2$. …

2: 4.15 Graphics

… ►Lines parallel to the real axis in the $z$-plane map onto ellipses in the $w$-plane with foci at $w=\pm 1$, and lines parallel to the imaginary axis in the $z$-plane map onto rectangular hyperbolas confocal with the ellipses. …

3: 4.24 Inverse Trigonometric Functions: Further Properties

… ►which requires $z$ $(=x+\mathrm{i}y)$ to lie between the two rectangular hyperbolas given by …

4: 4.38 Inverse Hyperbolic Functions: Further Properties

… ►which requires $z$ $(=x+\mathrm{i}y)$ to lie between the two rectangular hyperbolas given by …