A general geometry and calculus : including book I. of the general geometry, treating of loci in a plane; and an elementary course in the differential and integral calculus (1881)
Olney, Edward, 1827-1887 · New York : Sheldon and Co. · leaf 185
^ /d(p{x, y) dy dx dcp{x, y) \ dx + g. y)\ X J 0. But as by (2) dmF{x, y, q>{x, y)] = 0, and q){x, y) = m, this becomes — — \- CLvu dF{x, y, m)dy dy . dy -7-, whence -—dx dx locus. dF{x, y, m) dx dF{x, y, m)~ dy , the same as in the equation of the Ex. 4. Find the locus to which the hypot-… … 2atan BCX = , and the equation of BC is y = -X -\ . The equation sought is xy = -, the equation of an hyperbola. Ex. 5. What is the envelope of an ellipse which retains its axes inthe same right lines, but varies in eccentricity so that AB = a con-stant, 771 ? Sugs.—Since AB = m, the equation of…
Geometry, Analytic · Calculus
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