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

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a˛b˛ angle asymptotes ax˛ axes becomes bisects called centre CHAPTER chord chord of contact circle co-ordinates coincide conic section conjugate diameters constant corresponding cos˛ curve cuts denote described determined direction distance draw drawn ellipse equal example expression extremities figure find the equation fixed point focal focus given point giving Hence hyperbola inclined length line joining line passing locus meet middle point negative normal obtain origin pair parabola parallel perpendicular point of intersection polar equation pole positive preceding article produced proposition prove ratio rectangular referred represents respectively result right angles satisfy shew shewn sides similar Similarly sin˛ straight line Substitute suppose tangent tion touches triangle values vertex written y₁

### Popular passages

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 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.