Loney, S. L. (Sidney Luxton), 1860-1939 · London, Macmillan and co. · leaf 418
t the point (<x^^, 2a^)of this curve. Then ic = a (2 + Zf) and ^ = - latK (Art. 422.) .-. {x-2ay=21aH=^^ay\ i.e. the locus of the centre of curvature is the curve 21ay^ = i{x~2ay. This curve meets the axis of x in the point (20-, 0). It also meets the parabolawhere 27a2aj = (a;-2a)^i. e. where x… … 427. XT 11 Evolute of the ellipse —„ + ^„= 1.^ a^ ¥ If {x, y) be the centre of curvature corresponding to thepoint {ct, cos ^, b sin ^) of the ellipse, we have a-b^ x = cos^ <fi and y = — a -¥ sin^ <fi. 26—2 404 COORDINATE GEOMETRY. Hence {axf + (hyf = {a? - hf {cos^ «/, + sin^ </>} =…
Coordinates · Geometry, Analytic
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