An Elementary Treatise on Conic Sections by the Methods of Co-ordinate Geometry |
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Common terms and phrases
2hxy a² b2 angular points asymptotes ax² axes bisects by² centre centroid chord of contact circle x² circumscribing coefficients coincident conjugate diameters conjugate hyperbola constant cos² cross ratio curve diagonals director-circle directrix distance eccentric angles ellipse envelope find the equation find the locus fixed point fixed straight line foci focus four points given point given straight line imaginary infinite number inscribed latus rectum Let the co-ordinates Let the equation line joining line whose equation meet middle point nine-point circle normals origin orthocentre pair of conjugate parabola parallel chords pass perpendicular point of intersection point Q points of contact polar pole Prove quadratic equation quadrilateral radical axis radius ratio rectangular hyperbola required equation right angles S₁ self-polar shew sin² square subtend tangents triangle formed triangle of reference values vertex x²/a² y₁ y²/b² zero
Popular passages
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.