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 172
E LOCI. Differentiating the equation of the circle twice in succession we have (1) (a;-m) + (2/-n)^ = 0 In these equations and the general equation of the circle (3) {X — m)2 -j- {y — n)2 = r% dy d-y we can now substitute the values of y, -p, and ^-^ as obtained from the equation dx^ of the given… … (9) r = ± o+i:y cZx2 which substituted in (4) gives Substituting these values in (6) and reducing we have which is the formula for radius of curvature. The co-ordinates of the centre (m and n) are written at once from (8) and (7).They are , (10) m = a; — (11) n = y + (l + ^tW dx^/dx <Py , and l…
Geometry, Analytic · Calculus
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