Analytic geometry and principles of algebra (1913)
Ziwet, Alexander, 1853-1928, Hopkins, Louis Allen, joint author, Hedrick, E. R. (Earle Raymond), 1876-1943 · New York, The Macmillan Company · leaf 189
th P, x^ becomes equal to x, and y^ equal to y, so that the expression for tan a^ loses its meaning. But observing that P and Pi lie on the parabola, we have y- = 4 ax and ?/f = 4 a.i\ , and hence y^ — y~ = A:a(X]^ —x). Substituting from this relation the value of al — x in the above expression for… … Fig. 69 (■) tan a = y This slope of the tangent at P is also called the slojje of theparabola at P. The ordinate y of the parabola is a function ofthe abscissa x; and the slope of the parabola at P(x, y) is therate at which y increases with increasing a; at P; in other words,it is the derivative y…
Geometry, Analytic
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