A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic Sections

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Macmillan, 1862 - Conic sections - 326 pages

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Page 141 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Page 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 25 - In this equation n is the tangent of the angle which the line makes with the axis of abscissae, and B is the intercept on this axis from the origin.
Page 127 - A diameter of a curve is the locus of the middle points of a series of parallel chords.
Page 10 - Find the area of the triangle formed by joining the first three points in question 1. 5. A is a point on the axis of x and B a point on the axis of y ; express the co-ordinates of the middle point of AB in terms of the abscissa of A and the ordinate of B ; shew also that the distance of this point from the origin = ^ AB.
Page 268 - Two conic sections have a common focus 8 through which any radius vector is drawn meeting the curves in P, Q, respectively. Prove that the locus of the point of intersection of the tangents at P, Q, is a straight line.
Page 20 - To find the equation to a straight line in terms of the perpendicular from the origin, and the inclinations of the perpendicular to the axes.
Page 300 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Page 50 - ... proves the proposition. The lines drawn from the angles of a triangle perpendicular to the opposite sides meet in a point. The equation to BC is, (Art. 35), hence the equation to the line through A perpendicular to BC is, (Art. 44), y The equation to AC is ... (4).

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