When all the curves in a family G(x, y, c₁) = 0 intersect orthogonally all the curves in another family H(x, y, c₂) = 0, the families are said to be orthogonal trajectories of each other. See the following figure. If dy/dx = f (x, y) is the differential equation of one family, then the differential equation for the orthogonal trajectories of this family is dy/dx = -1/f (x, y). In Problem find the differential equation of the given family by computing dy/dx and eliminating c₁from this equation. Then ­find the orthogonal trajectories of the family. Use a graphing utility to graph both families on the same set of coordinate axes.

x² €“ 2y² = c₁

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