. Algebraic geometry; a new treatise on analytical conic sections . ion 3x-iy=J in the form xoos a+y sin a =p. The point to be observed here is that sin^a+cos%=l. Dividing through by s/Sl+i, by 5, the equation becomes 3x 4v 7 -= # = i, which is in the form 0 0 0 X 0O3 a + y sin a =p. r 3 . 4 3^ + 4^ 1 cosa=5, sina=-=, and sin^o + cos^a=—cj—= 1- The perpendicular on the given line from the origin makes an angletan~^ {--s) with the axis of x, and the length of this perpendicular is -funits. Example iv. Write the equation Aa; + By + C = 0 in the form a; cos a+ y sin a-^= the method of
. Algebraic geometry; a new treatise on analytical conic sections . ion 3x-iy=J in the form xoos a+y sin a =p. The point to be observed here is that sin^a+cos%=l. Dividing through by s/Sl+i, by 5, the equation becomes 3x 4v 7 -= # = i, which is in the form 0 0 0 X 0O3 a + y sin a =p. r 3 . 4 3^ + 4^ 1 cosa=5, sina=-=, and sin^o + cos^a=—cj—= 1- The perpendicular on the given line from the origin makes an angletan~^ {--s) with the axis of x, and the length of this perpendicular is -funits. Example iv. Write the equation Aa; + By + C = 0 in the form a; cos a+ y sin a-^= the method of Example iii., the required equation isAk By C \/As+B2 x/As+B -JA^ + B^ --0. 25. Given the equation of a straight line to draw this straight line to scale. [It is generally advisable to use squared paper.] This can be done by finding (by trial) the co-ordinates of two points on the straight line, and joining them. 24 THE STRAIGHT LINE. Example i. Draw the straight line 3k - 4y = this equation, when y=0, x=i; .: the point (4, 0) is on the line. [chap. It. Fia. 24. Plot this point, A in the figure. When !C=0, y--S; .: the point (0, - 3) is on the this point, B in the figure. AB is the straight line. ] THE STEAIGHT LINE. 25 Example li Draw the straight line y=ix + Z. When x=(i, y=Z; :. the point (0, 3) is on the line. Plot this point, C in the figure. Wheny=0, x= -J. The point (-|,0) is not very convenient to plot; we therefore findanother. When x=-2, y=-8 + 3=-5; .■. the point ( - 2, - 5) is on the line. Plot this point, D in the figure. CD is the line. Examples II. a. [The following Examples may be taken orally.\ Write down, or read off, in each case quoting the formula used, theequations of the following straight lines : 1. Parallel to, and at a, distance 8 from the axis of x, and on thepositive side of it. 2. Parallel to, and at a distance 5 from the axis of x, and on thenegative side of it. 3. Parallel to, andat a distance 4 from the axis of y,
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