 | Linnaeus Wayland Dowling, Frederick Eugene Turneaure - Geometry, Analytic - 1914 - 294 pages
...properties 120 DIAMETERS 101. Definition of diameter 123 102. Conjugate diameters ......... 123 103. The locus of the middle points of a system of parallel chords . 125 POLES AND POLAR LINES 104. Definition of pole and polar line 127 105. Geometric properties of... | |
 | Wallace Alvin Wilson, Joshua Irving Tracey - Geometry, Analytic - 1915 - 236 pages
...equal. Exercise 6. Show how to draw a tangent to an ellipse at any point. 143. Diameters of a Conic. — The locus of the middle points of a system of parallel chords of any conic is called a diameter of the conic. Let a chord with slope ui meet the ellipse in the points... | |
 | Charles Smith - Conic sections - 1916 - 466 pages
...The equation of the polar of O is gx +fy + c = 0 ; From (i) and (ii) we see that 1 * 2 183. To find the locus of the middle points of a system of parallel chords of a conic. Let (x, y') and (x'', y") be two points on the conic. The equation + b(yy')(y - y") = aa?... | |
 | Edward Harrison Askwith - Conic sections - 1917 - 302 pages
...central conies. The parabola has no centre and is called non-central. We have proved in § 95 that the locus of the middle points of a system of parallel chords is a straight line. Clearly in the case of the central conies this line must go through the centre, for... | |
 | George Alexander Gibson, Peter Pinkerton - Geometry, Analytic - 1919 - 510 pages
...points of the chords of the ellipse will lie on the straight line PGP. Hence we have (Fig. 117) THEOREM 3. The locus of the middle points of a system of parallel chords of an ellipse is a diameter of the ellipse, and the tangents to the ellipse at the ends of the diameter... | |
 | 1919 The Encyclopedia Americana Corporation - 1919 - 1190 pages
...curve (2) r = . 1 — cos 9 Diameter of the Parabola. — A diameter of any curve is defined to be the locus of the middle points of a system of parallel chords. Let (:TI, yt) and (xt, y*) be the co-ordinates of P, and Pi, the extremities of the chord Pi P, (Fig.... | |
 | Encyclopedias and dictionaries - 1919 - 936 pages
...curve (2) r = — . 1 — cos 8 Diameter of the Parabola. — A diameter of any curve is defined to be the locus of the middle points of a system of parallel chords. Let (x,, y,) and (x,, y,) be the co-ordinates of P, and Pi, the extremities of the chord Pi P, (Fig.... | |
 | Frederick Shenstone Woods - Geometry, Analytic - 1922 - 435 pages
...such that all chords through it are bisected by it. This is the center of the quadric. 2. Show that the locus of the middle points of a system of parallel chords is a plane which is the polar plane of the point in which the parallel chords meet the plane at infinity.... | |
 | Clarence Addison Willis - Geometry, Modern - 1922 - 318 pages
...finding the positions of a sufficient number of points to indicate the form of the complete locus. 1. The locus of the middle points of a system of parallel chords of a circle. 2. The locus of the middle points of all equal chords of a circle. 3. The locus of the... | |
 | Harvard University - Education - 1876 - 324 pages
...3. To find the equation of that chord of a conic which is bisected at the origin ; and to show that the locus of the middle points of a system of parallel chords is a right line. 4. The general equation of the tangents to a conic from a point (x 1 y') being U 1 U... | |
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The locus of the middle points of a system of parallel chords is the diameter perpendicular to them. 
