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Identifier: elementarytreati00bell (find matches)
Title: An elementary treatise on coordinate geometry of three dimensions
Year: 1912 (1910s)
Authors: Bell, Robert J. T. (Robert John Tainsh), 1877-1963
Subjects: Geometry, Analytic
Publisher: London : Macmillan and co., limited
Contributing Library: Wellesley College Library
Digitizing Sponsor: Boston Library Consortium Member Libraries

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il), we obtain the equation to the conoid. viz., z=f(y/x). Ex. 1. Find the equation to the right conoid generated by lineswhich meet OZ, are parallel to the plane XOY, and intersect thecircle x—a, i/i + s2 = r2. Ans. .r2(:2-r2) + aVJ = 0. b.g. R 258 COOKDINATE GEOMETRY (CH. XIII. Ex. 2. The graph of csin<9, from 0 = 0 to 0=2r7r, is wrapped round the cylinder x2+y2 = r2 so that the extremities of the graph coincide on OX. Lines parallel to the plane XOY are drawn to meet OZ and the curve so formed. Prove that the equation to the conoid they generate is -i-/ = sin-1-.x c r tan Ex. 3. Prove that if r = 2, the equation to the locus becomesz(x2 +y2) = 2cxy.(The locus is the cylindroid.)
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Pig. 51 Ex. 4. The curve drawn on the right cylinder x2+y2 = a2 so as tocut all the generators at the same angle is called the right circularhelix. The coordinates of any point on it are easily seen, (fig. 51),to be given by x=acosdi y=asin^ s = a0tana. The conoid generated by lines parallel to the plane XOY whichintersect the z-axis and the helix is the helicoid, (fig. 52). Shew thatits equation is 3==ctan-iy/^ where c = atmo,. Ex. 5. Lines parallel to the plane XOY are drawn to intersect OZ and the curves (i) x2+y2=r, -2+V2=- (ii) x2+y2 + z2- b2 a2 b2 c2 Find the equation to the conoids generated. yS, „2N / t2 y2\Am. (i) cr2(-2+f2) (ii) (&2-*2)(;- --2z(x2+y2), §177) SURFACES IN GENERAL Ex. 6. Discuss the form of the conoicU repn iented bj (i; v UtaPf (ii) v.; a - . Ex. 7. Conoids are constructed as in ESx. ^ with the graphi iricoHe*^, ctan ft Find their equations, consid Bcialiy the in which /• l and r = 2. Ana. vtan ■ cosec -, rt4n1-=tan1-. X c .<■ c r=\, <■-(.

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  • bookid:elementarytreati00bell
  • bookyear:1912
  • bookdecade:1910
  • bookcentury:1900
  • bookauthor:Bell__Robert_J__T___Robert_John_Tainsh___1877_1963
  • booksubject:Geometry__Analytic
  • bookpublisher:London___Macmillan_and_co___limited
  • bookcontributor:Wellesley_College_Library
  • booksponsor:Boston_Library_Consortium_Member_Libraries
  • bookleafnumber:281
  • bookcollection:Wellesley_College_Library
  • bookcollection:blc
  • bookcollection:americana
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30 July 2014

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