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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 definition 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 intercepts 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 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 205 - A PLANE is a surface, such, that if any two of its points be joined by a straight line, such.
Pāgina 182 - Find the locus of a point the sum of the squares of whose distances from the angular points of a given square is constant.
Pāgina 75 - PF' = 2 a. 97. Hence, an ellipse may also be defined as the locus of a point the sum of whose distances from two fixed points is constant.
Pāgina 70 - By definition [§ 69], the ellipse is the locus of a point whose distance from a fixed point, the focus, divided by its distance from a fixed line, the directrix, is a constant e, less than 1. Let F be the focus ,' and SR the directrix. Through F take А' я с A tsFD perpendicular to SR at D. There is a point A between F and D such that FA/AD = e.
Pāgina 185 - Prove that the locus of the poles of a given line with respect to a system of confocal conies is a line perpendicular to the given line.
Pāgina 191 - What are the relative positions of the following eight points: (a, b, c), (a, ft, - c), (a, - 6, c), (- a, b, c), (a, - 6, - c), (- a, b, - c), (- a, - 6, c), (- a, - 6, - c) ? Which of these points are symmetric with regard to the origin ? Which are symmetric with regard to the coordinate planes ? 236. Problem. To express the distance between two points P, P", in terms of their coordinates (x1, y', z'), (x", y", z"). Through P' and P" take planes parallel to the coordinate planes.
Pāgina 22 - Find also the point of intersection of the diagonals. 12. Find the equation of the line which passes through the point (2, — 3) and makes an angle of 60° with the x-axis.