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abscissa asymptotes avaxis axes axis called circle x2 coefficients coincide coincident points cone conic conicoid conjugate diameters conjugate hyperbola constant coordinate planes curve denote direction cosines directrix ellipse ellipsoid equa equal Example figure Find the equation Find the graph Find the locus fixed point foci focus given equation given line given points gives hyperbola hyperboloid intercept latus rectum left member length line joining line parallel line represented line segment meet mid-point negative obtained ordinate origin parabola y2 parametric equations passes perpendicular distance point of intersection point P(x polar coordinates positive projection Prove radical axis radius referred required equation respectively right angles roots satisfied second degree semiminor axis slope solution solving square straight line substitution surface symmetric tangent plane tion transformation triangle values vertex vertices x-axis y-axis z-axis
Sivu 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.
Sivu 184 - The locus of a point, the sum of the squares of whose distances from n fixed points is constant, is a circle.
Sivu 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.
Sivu 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.
Sivu 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.
Sivu 27 - Consider the circle whose center is at the origin and whose radius is a: (1) * + y1 = a'.
Sivu 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.
Sivu 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.