By Lewis Parker Siceloff, George Wentworth and David Eugene Smith

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Show that the equation of the locus of Pis (x- y) (x" + y 2 - 2 ax- 2 ay) = 0, and draw the locus. 18. The x intercept of the line y = 6- x is equal to the y intercept. 19. If the x intercept of the line y = ax - 3 is half the y intercept, find the value of a and draw the line. 20. If the graph of the equation x 2 - xy + ay2 = 23 passes through the point (3, - 2), find the value of a. 21. If the graph of the equation y = ax2 + bx passes through the points (- 1, - 3) and (2, 18), find the values of a and b.

20. 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.

22. Show that the graph of the equation y = log10 x approaches, in the negative direction, the y axis as an asymptote, a,nd draw the graph. A table of logarithms (page 284) may be used for plotting points close together on this graph. But if the student will recall the well-known logarithms of the numbers 1, 10, 100, ... 001, ... , he will see the character of the graph clearly after plotting a few of the corresponding points. 23. Show that the graph of the equation y = 2x approaches the x axis as an asymptote, and draw the graph.