An Elementary Treatise on Analytical Geometry, with Numerous by W J. Johnston

By W J. Johnston

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Express the following equations x + y= x^3 3, x >/3 + Ans. OC = 45°, p = 3 2. y. mx + m =Vi m + 2 3 = OC ; a =- % 20 330 sin OC T / , = o. p = = if, 3 p a= ; - o, 150°, ff x y - + <-=!. a b c, —==- y — 1 x + Vi + 2 bx Va cos ; = p , : xv 3-y+6 = o, form in the standard y = standard form + 210 3 in the -xV3 y+6 = o, 5 x — 12 y + 6-o, y — 6 - + y + — Va2 + b2 V 1 + nrr == = ab ay + + b2 m r» 2 Va 2 + b o. 2 PROJECTIONS 8 60i proof in § Deff is If the properties of projections are assumed, the statement of the 54 may — If A' be simplified.

Ix 4, + my = i. 4,-3; -7^4; ],~3. Find the Ans. x + y = line through 4. Find the line through is 18. Ans. x + y = area (3, 5) which cuts (3, 3) which forms with the axes a equal intercepts on the axes. off 8. triangle whose 6. STANDARD FORM § 54-. To express the equation to a straight line in terms of and 06 where p is the length of the perpendicular from the origin p 011 the line and OL is the angle which this perpendicular makes with the axis of x. AB be the line, ON = p, NOX = a. Let Let P be any point on the line x its = OM, co-ord's.

Is 3 x + = ijy=— c = - 5. y = 3 x - 5. by x Ax+ By + gives By = - C. Ax- C. C= 2 o, represents a . Geometry Analytical 32 B Suppose that I. not is = Then o. A dividing may be y=mx + written C, A the equation line passing II. B. we ; A x + By + C = through the point fo, an angle tan -1 f — B we put if m = -B' Thus by C x y = -B- -B this [51. o, C -A line parallel to OY at a distance Q — -r* here stand for any numerical quantities, signs included. Thus take the equation -3y Here A = 4, m Or we may go through •'• — 3Y + 4X — 1 4 § 51.

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