By Lewis Parker Siceloff, George Wentworth and David Eugene Smith
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How do the graphs of the two equations differ? 10. Show that the graph of the equation xy = 0 consists of the x axis and the y axis. 11. Draw the graph of the equation (x2 + y 2) 2 - 9 x2 = 9 if. 53 INTEHSECTIONS OF GRAPHS 55. Intersections of Graphs. The complete solution of two simultaneous equations in x and y gives all pairs of values of the unknowns that satisfy both equations. Moreover, every pair of values of x and y that satisfies both equations locates a point of the graph of each equation.
As x increases numerically from 0 to 5, y decreases numerically from 3 to 0. From this examination of the equation we see that it is necessary to locate the points merely in the first quadrant, draw the graph in that quadrant, and duplicate this m the other quadrants. 8 0 --- --- SYMMETRY 43 43. Symmetry. freely employed in § 42. We shall, however, use the word frequently as we proceed, and hence it is necessary to define it and to consider certain properties of symmetry. Two points are said to be symmetric with respect to a line if the line is the perpendicular bisector of the line segment which joins the two points.
3 x 2 - xy- 4 x + y = 7. 11. f -x 4 8. -4-= . 12. y 2 (5 10. + x)=- x 8• 13. y (3+x)=x (3-x). 2 2 14. f(x-4)-x2 (x-8)=0. 15. x 2(y+8)+y3 =0. 16. f. 17. 2 :J =9(x2-2x-8). ~-6x+5 18. y = ') x-4 2 """'x- 7 x- 4 19. A and Bare two centers of magnetic attraction 10 units apart, and P is any point of the line AB. P is attracted by the center A with a force P1 equal to 12/A P 2, 10 and by ~e center B with a force F 2 equal ~to 18jBP2• Letting x=AP, express in terms of x the sum s of the two forces, and draw a graph showing the variation of s for all v::Llues of ;::;, 52 LOCI AND THEil~ EQUATIONS 54.