By Gordon Fuller, Dalton Tarwater
|Tailored for a primary direction within the learn of analytic geometry, the textual content emphasizes the basic parts of the topic and stresses the suggestions wanted in calculus. This re-creation used to be revised to offer the topic in a contemporary, up to date demeanour. colour is used to focus on suggestions. expertise is built-in with the textual content, with references to the Calculus Explorer and assistance for utilizing graphing calculators. numerous new themes, together with curve becoming related to mathematical modeling have been extra. workouts have been up-to-date. New and sundry functions from drugs to navigation to public overall healthiness have been added.|
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Additional info for Analytic Geometry
See #(8, -5), and C(5,4). ) Solution. formula (1), The slopes we get A( -2,3) of the sides are indicated in Fig. 2-11. C(5,4) 5(8, -5) FIGURE 2-11 Substituting in FUNDAMENTAL CONCEPTS AND FORMULAS 26 [CHAP. 2 B=33 C - - 100'. EXERCISE 2-2 1. Give the slopes for the inclinations Find the slope of the 2. 4. line passing (a) 45; (b) 0; (c) 60; (d) 120; (e) 135. through the two points in each problem 2-7 (2,3), (3,7). 3. (6, (-4,8), (7,-3). 5. (5,4), 6. (0,-9), (20,3). 7. (4,12), 8. Show that each -13), : (0,5).
3 5(2) + ' 12(1) 13 + C _ ~* Hence the required equations are and 5z + I2y - 61 - 0. 3-6 Family of lines through the intersection of two lines. The equation of the family of lines passing through the intersection of two given lines can be written readily. To illustrate, we consider the two intersecting lines From the left members (2* of these equations - 30 we form + 5) + fc(4x + y - 11) the equation - 0, (1) THE STRAIGHT LINE 42 where a parameter. is fc This equation Hence is [CHAP. 3 of the first degree in x and y represents a system of lines.
Or 1), SPECIAL FORMS OP THE FIRST DEGREE EQUATION 3-3] = D Alternatively, we notice that 4x real value of D. To determine + 3y substitute these coordinates for x and y and obtain D 4(-l) By EXAMPLE A (3,2) 2. and A point (5,6). parallel to the given line for is so that the line shall pass through + 3(3) we have again using 5 for D, 35 = or />, the equation 4x moves so that it is Find the equation of + D= 5. = 5. 3z/ any we 1,3), ( equally distant from the two points its locus. From plane geometry we know that the locus is the line perpendicular Solution.
Analytic Geometry by Gordon Fuller, Dalton Tarwater