By Gordon Fuller, Dalton Tarwater
|Tailored for a primary direction within the research of analytic geometry, the textual content emphasizes the fundamental components of the topic and stresses the thoughts wanted in calculus. This re-creation used to be revised to give the topic in a latest, up-to-date demeanour. colour is used to spotlight options. know-how is built-in with the textual content, with references to the Calculus Explorer and counsel for utilizing graphing calculators. numerous new issues, together with curve becoming related to mathematical modeling have been extra. routines have been up-to-date. New and sundry purposes from medication to navigation to public overall healthiness have been added.|
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Additional resources for Analytic Geometry
Both sets of axes and the graph are drawn in Fig. 4-2. EXAMPLE 2. Translate the axes so that the equation 2z 2 is + 3# 2 - 10* + ISy + 26 - transformed to a simpler form. Solution. we use We do not know in advance what the translation should be. the translation formulas with h and k unknown. Thus we have Hence 47 TRANSLATION OF AXES 4-2] Y' 0' (-2,3) FIGURE 4-2 2(x' 2x' 2 -f 3i/ 2 We 6& + + 3(y' + k)* - 10(x' + + - 10)*' + (6* + 18)//' + 2fc + 3* + h)* fc) 2 (4/i and set the coefficients of x' + 18 equation = and hence h 0, = 2 equal to zero.
16. (0,0) intersects the line through THE MID-POINT OP A LINE SEGMENT 2-5] 17. Two of the lines 18. lines passing is 2, What through (2,3) make an angle of 45. Two find the slope of the other. 2-5 The mid-point of a line segment. If the slope of one solutions. make with a angle does a line of slope 27 vertical line? Problems in geometry make use of the mid-points of line segments. We shall derive formulas which give the coordinates of the point midway between two points of much given coordinates.
3 + 2y + 4 + 7y = 0. 5. 8. By inspection, give the slope tions 13-24. - 15. x +y+ 12. 18. 6* 14. 21. 7x 4. 24. - 3y by equa- 4 = - 10 + 3z/ + 3* + 3y = 6 0. = 0. = 0. 1. In each problem 25-36, write the equation of the line determined by the slope m and the ^-intercept 6. 25. m = 3; b = -4. 27. m = -4; b = 5. 29. m = 6 - -2. = 31. m 0; 6 = -6. 33. m = -J; 6 = -8. 35. m = 0; b = 0. ; 26. 28. 30. 32. 34. 36. = 2; 6 = 3. = -1;6 = 1. = $ 6 = -6. -5; 6 = 0. = 0; b = -2. m = - 6 = 0. m m m m m ; ; THE STRAIGHT LINE 36 Write the equation of the problem 37-48.
Analytic Geometry by Gordon Fuller, Dalton Tarwater