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 163
tersections with the axes may also be of service. Ex. 1. Trace the curve whose equation isy2 — 2a;y + 2^7* + 2?/ + a? + 3 = 0. Sugs.—Since B^ — 4:AC <^ 0, the locus is an el-lipse. Solving for y, we have y = OS — 1 ± \/— .r2 — Sx — 2 ;whence y = x — 1 is a diameter, which we construct. n/— x- —… … Fig. 139. Ex. 2. Trace the curve whose equation is t/2 -|- 2xy — 2x^ — 4?/ —07 + 10 = 0. Sugs.—As B^ — iAC >* 0 the locus is an hy-perbola. ?/ = —^ + 2drv/3(x2—iP — 2). y = — X-f- 2 locates N M. From 3(aj^ — x — 2) = 0, wefind P and P , at .r =-- 2, and — 1. Betweenthese values y is imaginary ;…
Geometry, Analytic · Calculus
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