Coordinate GeometryMacmillan, 1909 - 297 pàgines |
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Frases i termes més freqüents
a² b2 abscissa asymptotes ax² axes axis bisects by² called chords circle x² coefficients coincident points cone conic conicoid conjugate diameters conjugate hyperbola constant 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 line gives Hence hyperbola hyperboloid k₁ k₂ latus rectum left member length line joining line segment meet mid-point negative O₁₁ obtained origin P₁ pair parabola y² parallel parametric equations passes perpendicular perpendicular distance point of intersection point P(x polar polar coordinates positive projection Prove rectangular referred represents required equation respectively roots second degree semimajor axis sin² slope solution square straight line substitution surface tion transformation triangle values vertex x-axis x₁ x²/a² xy-plane y-axis y₁ y²/b²
Passatges populars
Pàgina 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.
Pàgina 168 - 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.
Pàgina 205 - A PLANE is a surface, such, that if any two of its points be joined by a straight line, such.
Pàgina 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.
Pàgina 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.
Pàgina 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.
Pàgina 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.
Pàgina 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.
Pàgina 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.
Pàgina 200 - 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.