Mathematics for engineering students, Analytical geometry and calculus (1907)
Keller, S. S. (Samuel Smith), 1867-1923, Knox, W. F., [from old catalog] joint author · New York : D. Van Nostrand company · leaf 99
system of parallel chords. 90 Analytical Geometry. Draw (Fig. 35) a series of chords (like CD) || to eachother. To determine the locus of the middle points ofthese chords, that is, the diameter corresponding to them. Let the equation of any one of the chords, as CD, be and y y = mx2 2 px (1), (2)… … Fig. 35. (mx + b)2 = 2 px,m2x2 + 2 mbx + b2 = 2 px, x2 + (2 mb — 2 p) x m (3) Now in a quadratic of the form z2 + az + b = o, the sum Analytical Geometry. 91 of the two values of the unknown equals the coefficient (a)of the first power of the unknown with its sign changed.* Hence the two values of…
Geometry, Analytic · Calculus
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