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 126
ent to a?iy plane curve is f in which (x, y) is the point of tangency, and x and j are the currentco-ordinates of the tangent. Dem.—Let MN, Fig. 98, be any planecurve whose equation is y =f(x), and let Pbe the point of tangency whose co-ordinatesare x, y. Now, the equation of any linepassing… … Fig. 98. ting, we have y — y =■ ^{x X). l. E. D. Ex. 1. What is tlie equation of a tangent to an ellipse referred toits axes? Solution.—The equation of the locus is A^y- -\- B^x^ = A^B^; whence y^ = — B-x B^x dv —r—, which satisfied for the point (x\ y) is -—. Substituting this value of — in the…
Geometry, Analytic · Calculus
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