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abscissa Asymptotes axes of co-ordinates bisect centre Chapter Chord joining circle CONIC SECTIONS conjugate diameters conjugate hyperbola cut the axis denoted diameter be drawn directrix equal equation required fall the perpendicular find the equation find the intersection find the locus fixed point Focal Distances focus given angle given in position given point given straight line Harmonic Mean Hence Hugh James Rose indeterminate equation joining the points latus rectum let fall M.A. Fellow major axis middle points ordinate pairs of tangents parabola parallel chords parallel to AX point of intersection points of contact polar equation principal proved rectangle contained rectangular right angles second degree Second Edition straight line given substitution subtangent supplemental chords supposed System of Conjugate tangents be drawn Temple Chevallier TREATISE Trinity College University of Cambridge values vertex
Page 97 - ... a diameter, in a constant ratio, the author proves the following propositions relating to this curve : — 1. The rectangle of the abscissae is to the square of the ordinate, as the square of the semiaxis major to the difference of the squares of the semiaxis major and the excentricity. 2. The distance of any point in the curve from the focus, is to its distance from the directrix, as the excentricity is to the semiaxis major. 3. The sum of the distances of any point in the curve from the two...