An Elementary Treatise on Conic Sections by the Methods of Co-ordinate Geometry

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Macmillan, 1916 - Conic sections - 449 pages
 

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Page 122 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 176 - A'P, C being the centre of the curve. 3. A point moves so that the sum of the squares of its distances from two intersecting straight lines is constant.
Page 185 - The hyperbola is the locus of a point which moves so that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line, the ratio being greater than unity.
Page 103 - A point moves so that the sum of the squares of its distances from the four sides of a square is constant.
Page 39 - The three straight lines joining the angular points of a triangle to the middle points of the opposite sides meet in a point. Let the angular points A , B, C be (x', y'), (x", y") , (x"', y"') , respectively. Then D, E, F, the middle points of BC, CA, AB respectively, will be fx"+x"' y"+y"'\ (x"' + x' y"' + y'\ , fx
Page 109 - A conic section is the locus of a point which moves so that its distance from a fixed point, called the focus, is in a constant ratio to its distance from a fixed straight line, called the directrix.
Page 20 - To find the equation of a Straight line in terms of the intercepts which it makes on the axes.
Page 347 - ... by the square root of the sum of the squares of the coefficients of x and y.
Page 114 - To find the locus of the point of intersection of two tangents to a parabola which are at right angles to one another.
Page 339 - ... given by the equation ax* + 2,gx = 0 must be zero ; therefore g = 0. Hence the most general form of the equation of a conic, when referred to a tangent and the corresponding normal as axes of x and y respectively, is ax* + 2hxy + by* + 2fy = 0.

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