Coordinate Geometry

Macmillan, 1909 - 300 sivua

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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 170 - The cycloid. This is the curve traced by a point on the circumference of a circle, when the circle is made to roll (without sliding) on a straight line.
Sivu 207 - A PLANE is a surface, such, that if any two of its points be joined by a straight line, such.
Sivu 184 - Find the locus of a point the sum of the squares of whose distances from the angular points of a given square is constant.
Sivu 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.
Sivu 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.
Sivu 187 - 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.
Sivu 193 - 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.
Sivu 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.
Sivu 202 - What are the coordinates of the point of intersection ? 12. 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.