An Elementary Treatise on Conic Sections |
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Common terms and phrases
2hxy a² b2 angular points asymptotes ax² bisect by² centre coefficients coincident confocal conics conic touching conjugate diameters conjugate hyperbola corresponding cross ratio curve diagonals director-circle directrix distance eccentric angles ellipse envelope equal angles find the equation find the locus fixed point fixed straight line foci focus four given points four points given conic given straight line imaginary inscribed latus rectum Let the co-ordinates Let the equation line joining line whose equation meet middle point nine-point circle normals original conic pair of conjugate parabola perpendicular point h point of intersection points at infinity points of contact polar pole prove quadrilateral radical axis radius reciprocal rectangular hyperbola required equation respect right angles second degree shew sides sin² square tangents triangle formed triangle of reference values vertex x² y² zero
Popular passages
Page 100 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 138 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 31 - Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line.
Page 146 - 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 282 - ... by the square root of the sum of the squares of the coefficients of x and y.
Page 88 - 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 112 - It may also be defined as the locus of a point which moves so that its distance from a fixed point is in a constant ratio to its distance from a fixed straight line.
Page 313 - A parabola touches one side of a triangle in its middle point, and the other two sides produced ; prove that the perpendiculars, drawn from the angular points of the triangle upon any tangent to the parabola, are in harmonical progression.
Page 274 - Prove that chords of a conic, which subtend a right angle at a fixed point 0 in the conic, pass through a fixed point on the normal at 0.
Page 15 - To find the equation of a straight line in terms of the intercepts which it makes on the axes.