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angle asymptotes axes axis becomes called chords circle coefficients coincide common condition cone conic conicoid conjugate constant coordinates corresponding curve cuts denote determined diameter direction cosines directrix distance divided drawing ellipse equal Example Exercises expression figure Find the equation foci focus given given line gives graph Hence hyperbola indicated length lies line joining line segment locus meet method mid-point namely negative normal obtained opposite origin pair parabola parabola y2 parallel passes perpendicular plane point of intersection polar positive produced projection Prove radius ratio rectangular reduced referred relation represents required equation respectively result roots satisfied second degree side Similarly slope solution solving square straight line substitution surface symmetric taken tangent tion touches transformation triangle true values vertex vertices written x-axis y-axis
Pāgina 39 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Pāgina 184 - The locus of a point, the sum of the squares of whose distances from n fixed points is constant, is a circle.
Pāgina 170 - The right cycloid is the curve traced by a point on the circumference of a circle which rolls without sliding upon a fixed straight line in the same plane.
Pāgina 163 - The cissoid was used to solve the problem of the duplication of the cube, that is, of finding the edge of a cube whose volume is twice that of a given cube, one of the famous problems of antiquity.
Pāgina 75 - From the definition of an ellipse, as the locus of a point the sum of whose distances from two fixed points is constant, •shew that the ellipses are similar when the eccentricities are the same.
Pāgina 27 - Consider the circle whose center is at the origin and whose radius is a: (1) * + y1 = a'.
Pāgina 22 - Find the equation of the line which passes through the point (0, 5) and makes an angle of 60° with the positive direction of x-axis.
Pāgina 202 - Find the coordinates of the mid-point of the line segment joining the points (5, — 2, 7) and (2, 2, — 5); also the coordinates of the points where this line segment is trisected.