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

By Lewis Parker Siceloff, George Wentworth and David Eugene Smith

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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. Degenerate Equation. It occasionally happens that when all the terms of an equation are transposed to the left member that member is factorable.

A function obtained by applying to x one or more of the algebraic operations (addition, subtraction, multiplication, division, and the extraction of roots), a limited number of times, is called an algebraic function of x. For example, x 3, _x_, and 3 x 2 tions of x. Vl- x are algebraic func- x 59. Transcendent Function. If a function of x is not algebraic, it is called a transcendent function of x. Thus, log x and sin x are transcendent functions of x. 60. Important Functions. Although mathematics inclmles the study of various functions, there are certain ones, such as y = ax", which are of special importance.

0, 0), (0, 3. (- 3, 1), (2, 7). -§-). Find the mid point of each of these line segments, the end points being as follows : 7. 3). 9. 2). 8. 2). 10. )· c Find the point which divides eaclt of these line segments in the rcitio stated, drawing the figure in each case : 11. (2,1)to(3,-9); 4:1. 12. (5, - 2) to (5, 3); 2: 3. 13. (-4, 1) to (5, 4); -5:2. ~, 14. (8, 5) to ( -13, - 2); 4: 3. Find the two trisection points of each of these line segments, the end points being as follows : \_ 15. (-1,2),(-10,-1).

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