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

Macmillan, 1862 - Conic sections - 326 pages

Contents

 PLANE COORDINATE GEOMETRY 1 V 11 Problems on the Straight Line 25 Straight Line continued 58 The Circle 84 Radical Axis Pole and Polar 104 The Parabola 112 The Ellipse 141
 The Ellipse continued 168 The Hyperbola 189 The Hyperbola continued 203 General Equation of the Second Degree 227 Miscellaneous Propositions 247 Abridged Notation 274 Sections of a Cone 300

Popular passages

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).