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

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Macmillan, 1858 - Conic sections - 316 pages

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Page 187 - Hyperbola is the locus of a point which moves so that its distance from a fixed point, called the focus, bears a constant ratio, which is greater than unity, to its distance from a fixed straight line, called the directrix.
Page 98 - 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 139 - 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 32 - To find the equations to the straight lines which pass through a given point and make a given angle with a given straight line.
Page 227 - Put x = x cos 0 — y sin 0, y = x
Page 266 - S 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. Shew that this straight line passes through the intersection of the directrices of the conic sections, and that the sines of the angles which it makes with these lines are inversely proportional to the corresponding excentrities.
Page 10 - Art. 11 so as to give an expression for the area of a triangle in terms of the polar co-ordinates of its angular points.
Page 294 - 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.

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