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Elements of Coordinate Geometry

Elements of Coordinate Geometry


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About the Book

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1902 edition. Excerpt: ...found to be V (h + 2) = 2a; + 2at1t2. The tangents at the points (at?, 2at and (at.?, 2at2) are ty = x + at?, and ty--x + at?. The point of intersection of these two tangents is clearly atxt2, a (t1 + t2). The point whose coordinates are (at2, 2at) may, for brevity, be called the point "t." In the following articles we shall prove some important properties of the parabola making use of the above substitution. and the equation to the straight line through the intersection of (1) and (2) perpendicular to (3) is x /l 1 1;/ +--=---+--+ (6. The point which is common to the straight lines (4), (5), and (6), i.e. the orthocentre of the triangle, is easily seen to be the point whose coordinates are 1. If a be the angle which a focal chord of a parabola makes with the axis, prove that the length of the chord is 4a cosec-w and that the perpendicular on it from the vertex is a sin w. 2. A point on a parabola, the foot of the perpendicular from it upon the directrix, and the focus are the vertices of an equilateral triangle. Prove that the focal distance of the point is equal to the latus rectum. 3. Prove that the semi-latns-rectum is a harmonic mean between the segments of any focal chord. 4. If T be any point on the tangent at any point P of a parabola, and if TL be perpendicular to the focal radius SP and TN be perpendicular to the directrix, prove that SL = TN. Hence obtain a geometrical construction for the pair of tangents drawn to the parabola from any point T. 5. Prove that on the axis of any parabola there is a certain point K which has the property that, if a chord PQ of the parabola be drawn through it, then 1 1 is the same for all positions of the chord. 6. The normal at the point (a2, 2atj) meets the parabola again in the...


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Product Details
  • ISBN-13: 9781231721223
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 76
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1231721227
  • Publisher Date: 01 Oct 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 154 gr

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