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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §4.2 Implicit Differentiation and Related Rates, #11 · Calculus · Related rates

Show that the hyperbolas … are perpendicular to the hyperbolas

Show that the hyperbolas $x y = C$ are perpendicular to the hyperbolas $x^{2} - y^{2} = D$ . (Perpendicular means that the product of slopes is $- 1$ .)

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §4.2 Implicit Differentiation and Related Rates, #11

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