A Short Course in College Mathematics Comprising Thirty Six Lessons On Algebra
A Short Course in College Mathematics Comprising Thirty Six Lessons On Algebra
Robert Douard Moritz
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On the same sheet of paper draw the four lines : y-x = lj y + x=\, 2/ = l, x = (d. 3. Write the equation of the line which cuts the ?/-axis 5 units below the origin and makes an angle of 45 with the positive direction of the aj-axis. 4. Show that if two lines are perpendicular the product of their slopes is 1, that is, if the equations of the two lines are y z=z mx + b, and y = m'x -f 5', then mm' = 1, or m' = 1/m. 5. Write and simplify the equations of the following circles : (a) Center at (3,... 4), radius 5 ; (6) Center at (3, 4), radius 4; (c) Center at ( 3, 4), radius 1; (d) Center at (5, 0), radius 5 ; (e) Center at (0, 10), radius |; (/) Center at origin, radius r. Ans. (a) x'^ 6x-\-y'^ Sy = 0; (b) x^-{-6x + y^-Sy + 9 = 0', etc. 6. Determine the coordinates of the center and the length of the radius of each of the following circles : 96 A SHORT COURSE IN MATHEMATICS (a) a;2 + 2/2 = 2 ; {d) x^ -^x-y-'^O-, (b) ic2_ 4a; + 2/2 -6^4- 12 = 0; (e) 4 a;2_|_ 12 a; + 4 2/2 - 91 = 0; (c) x^-\-2x-\-y^-\-2y=:0', (/) 3a;2 _ 5 a; + 32/" + 62/=-3.
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