A Course in Mathematics, for Students of Engineering and Applied Science Volume 1

A Course in Mathematics, for Students of Engineering and Applied Science Volume 1

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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. 1907 edition. Excerpt: ...is drawn parallel to the conjugate axis, then PQ. PR =--b2. 105. Show that the focal distance of any point on the hyperbola is equal to the length of the straight line drawn through the point parallel to an asymptote to meet the corresponding directrix. 106. Prove that the product of the distances of any point of the hyperbola from the asymptotes is constant. 107. Prove that in the hyperbola the squares of the ordinates of any two points are to each other as the products of the segments of the transverse axis made by the feet of these ordinates. 108. Lines are drawn through a point of an ellipse from the two ends of the minor axis. Show that the product of their intercepts on OX is constant. 109. Pi is any point of the parabola y2 = 4px, and PiQ, which is perpendicular to OPi, intersects the axis of the parabola in Q. Prove that the projection of PiQ on the axis of the parabola is always 4p. CHAPTER VIII INTERSECTION OF CURVES 86. General principle. If fm(x, y) is an expression involving xaniy'. / y)-0 (1) is the equation of a curve containing all points the coordinates of which satisfy (1), and containing no other points. Similarly if fn(x, y) is any second expression in x and y, yy)=o (2) is the equation of a second curve. It follows that if we consider these two equations, any point common to the two corresponding curves will have coordinates satisfying both (1) and (2); and that, conversely, any values of x and y which satisfy both (1) and (2) are coordinates of a point common to the two curves. Hence, to find the points of intersection of two curves, solve their equations simultaneously. We have already discussed in 30 the simplest case of this problem, i.e. the intersection of two straight lines. We shall now discuss...show more

Product details

  • Paperback
  • 189 x 246 x 4mm | 145g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236981499
  • 9781236981493