By Lewis Parker Siceloff, George Wentworth and David Eugene Smith

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Find the equation of the y axis. 21. The points (1, 1), (2, 0), (0, 2) lie on a straight line. 36 LOCI AND THEIR EQUATIONS 36. Equation of a Circle. The general equation of the circle with a given center and a given radius is easily deduced after considering a special case. Let 0(2, 3) be the center and 7 the radius of a given circle. Then if P(x, y) is any point on the circle, we have whence and CP= 7, (x- 2)2+ (y- 3) 2 = 49, y ~-..... XI-+ y 2 - 4 x- 6 y = 36, which is true for all points (x, y) on the circle and for no other points.

Then we have that is, slope of QP =slope of l; 11- b _v _ _ =m; x-0 y=mx+b. whence § 21 This equation is called the slope equation of the line. When m 0, then y = b, and the line is parallel to the x axis. ·when b = 0, then y = mx, and the line passes through the origin. When m = b = 0, then y = 0, and the line coincides with the x axis. Since the y intercept is given, the line cuts the y axis, and the equation y = mx + b cannot represent a line which is perpendicular to the x axis.

If the first of two quantities depends upon the second in such a way as to be determined when the second is given, the first quantity is called a Junction of the second. For example, x 2 , VI - x, and ax log x are functions of x. In the case of A= 1rr2, A is a functiou of r, and 1· is a function of A. Every equation in x and y defines a functional relation. For example, the equation 4 x 2 - y2 = 25 defines // as a function of x, for y = -Y4 x 2 - 25. It also defines x as a function of y. 55 FUNCTIONS 58.

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Analytic geometry by Lewis Parker Siceloff, George Wentworth and David Eugene Smith


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