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abscissa asymptotes axes are oblique axis of X becomes bisects centre chord of contact coefficients coincident coincident points confocal conic conjugate diameters conjugate hyperbola conjugate points constant coordinate axes corresponding cos2 curve cuts denote diagonals direction parameters directrix drawn eccentric angle ellipse equa equal external bisectors Find the equation Find the length find the locus fixed point focal distances foci focus given circles given line given point x'y imaginary intercepts latus-rectum line joining loci major auxiliary circle major axis meet middle points opposite sides ordinate origin pair of conjugate parabola y2 perpendicular point of intersection point P(xy points of tangency polar coordinates polar equation pole positive radical axis ratio rectangular axes represents required equation roots secant Show sin2 squares straight line passing subtangent system of conies tangent tangent and normal tlhe transverse triangle Trigonometry trilinear coordinates values vertex vertices zerg
Página 137 - 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.
Página 344 - Many theorems are proved both by the method of rates and that of limits• and thus each is made to throw light upon the other. The chapter on differentiation is followed by one on direct integration and its more important applications. Throughout the work there are numerous practical problems in Geometry and Mechanics, which serve to exhibit the power and use of the science, and to excite and keep alive the interest of the student.
Página 178 - Conic, is 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. The fixed point is called a focus, the fixed straight line is called a directrix, and the constant ratio is called the eccentricity.
Página 176 - The locus of a point, the sum of the squares of whose distances from n fixed points is constant, is a circle.
Página iii - TN this work, the author has had particularly in mind the needs of those students who can devote but a limited time to the subject, and yet must become quite familiar with at least its more elementary and fundamental part. For this reason, the earlier chapters are treated with somewhat more fulness than is usual. For some propositions, more than a single proof is given, and particular care has been taken to illustrate and enforce all parts of the subject by a large number of numerical applications....