Schmall, Charles Nelson. [from old catalog] · New York, D. Van Nostrand company · leaf 64
ine revolves around a fixed point O,meeting a given line PM in a point P. Find the locus of the point Q inthe revolving line so that OP • OQ = k^. Take 0 as the pole, and OM ± to PM as polar axis. Let the point Qbe (p, 6), and let OM = a. Then o = OP cos 6. * When a line revolves about a fixed… … Fig. 57. ■ cos 6,Pap = k^ cos d,which represents the required locus. Note. — To transform to rectangu-lar co-ordinates, this result may bewritten : a p^ = k^ • p cos ^, or a {x^ + y^) = k^x, which shows that the locus of the point Q is a circle. Ex. 30. Trace the locus of the equation p = 2a cos ^,…
Geometry, Analytic
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