Coordinate Geometry of Two Dimensions by Hari Kishan

By Hari Kishan

The current booklet Coordinate Geometry of 2 Dimensions goals at delivering the scholars with a close research of Polar Coordinates, Polar Equations of a immediately Line and a Circle, Polar Equations of Conics, common Equation of moment measure and process of Conics? -- the subjects incorporated within the UGC syllabus. essentially intended for college kids of B.Sc./B.A. of numerous Indian Universities, the ebook precisely covers the prescribed syllabus. It neither contains the inappropriate nor escapes the basic issues. Its method is explanatory, lucid and accomplished. The analytic rationalization of the subject material is particularly systematic which might let the scholars to evaluate and thereby resolve the comparable difficulties simply. adequate variety of high-graded solved examples supplied within the e-book facilitate larger figuring out of many of the abilities valuable in fixing the issues. moreover, perform workouts of a number of kinds will absolutely turn out necessary in quickly revision of the topic. The figures and likewise the solutions supplied within the ebook are actual and established completely. a formal examine of the ebook will certainly convey to scholars a super good fortune. Even academics will locate it valuable in elucidating the topic to the scholars of arithmetic.

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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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