Elements of Analytic Geometry

Cover Elements of Analytic Geometry
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Then have ^'^ PQ ^ PE cos e. (a) Y P K\ / 5>r "^ /Q M.
THE STRAIGHT LINE. 45 Now R is a point on tlie line whose abscissa is the same as that of P, namely, x'] and if we put RM = y^ = the ordi- nate of R, we must have, since R is on the line, Ax^ -{. Bt/, -^ C = 0, , . , . Ax' -i- C which gives y^ = h • Then PR = PM - RM = y' - y^ _B£_ _ Ax' -{. By' -^r O ~ B ^' ~ B Substituting in {a) this value of PR and the value of cos e from (13), we have ^ VA' -{- B' ^ ^ Since the co-ordinates of the orig
...in are x' = and y' = 0, we have OQ' =, ^ -- (15) VA' -{- B' ^ ^ which gives the perpendicular from the origin on the line.
EXERCISES.
Find, for each of the lines represented by the following equations, — The angle which it makes with the axis of X; Its intercepts upon the axes; Its distance from the point (4, 3); Its least distance from the origin; The length of that portion, intercepted between the axes.
1. 3a; + 4?/ + 10 = 0. 2. Sx + 4?/ - 10 = 0.
3. 6x — 12y 4- 26 = 0. 4. A; + ?/ = 0.
5.


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