By Lewis Parker Siceloff, George Wentworth and David Eugene Smith

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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.

7. 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.

15. If P (5, 9) is on a circle whose center is (1, 6), find the radius of the circle and the slope of the tangent at P. 16. The points (8, 5) and (6,- 3) are equidistant from (3, 2). 17. Given A(2, 1), B(3,- 2), and C(- 4, -1), show that the angle BA C is a right angle. 18. The line through (a, b) and (c, cl) is perpendicular to the line through (b, -a) and (cl, -c). · ,, 19. Draw the triangle A ( 4, 6), B (- 2, 2), C (- 4, 6), and show that the line joining the mid points of AB and A C is parallel to BC and equal to half of it.