An elementary treatise on conic sections |
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An Elementary Treatise on Conic Sections by the Methods of Co-Ordinate Geometry Smith Charles No preview available - 2019 |
Common terms and phrases
2hxy a² b2 angular points asymptotes ax² bisects by² centre coefficients coincident confocal conics conic touching conjugate diameters conjugate hyperbola constant 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 lines foci focus four points given conic given straight line harmonic imaginary inscribed latus rectum Let the co-ordinates Let the equation line joining line whose equation meet middle point nine-point circle normals pair of conjugate parabola Pascal's Theorem pencil perpendicular point of intersection point Q points at infinity points of contact polar pole projection prove quadrilateral radical axis radius reciprocal rectangular hyperbola required equation 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 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 29 - The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point.
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 93 - To find the locus of the point of intersection of two tangents to a parabola which are at right angles to one another.
Page 262 - 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.