 | Alfred Clement Jones - 1903 - 212 pages
...the y-coordinate of the middle points of parallel chords of a parabola is constant ; in other words, the locus of the middle points of a system of parallel chords of a parabola is a straight line parallel to the axis. This locus is called a diameter ; hence all... | |
 | Frederick Converse Beach - 1904 - 914 pages
...curve (2) r = - • I — cos в 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 (xt, J>i) and (.r-, y~) be the co-ordinates of P, and P:, the extremities of the chord Pi Pi (Fig.... | |
 | Euclid - 1904 - 488 pages
...The line joining the middle points of two parallel chords of a circle passes through the centre. 11. Find the locus of the middle points of a system of parallel chords drawn in a circle. 12. If two circles cut one another, any two parallel straight lines drawn through... | |
 | Albert Luther Candy - 1904 - 288 pages
...approach zero is the tangent of half the angle between the lines. 117] THE ELLIPSE AND HYPERBOLA 117. To find the locus of the middle points of a system of parallel chords of a central conic. I. Let AB be any one of a system of parallel chords of the ellipse Let P(x', y')... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale - 1904 - 462 pages
...varies so that B1 — 4 AC approaches zero, how does the center of the locus behave ? 98. Diameters. The locus of the middle points of a system of parallel chords of a curve is called a diameter of the curve. Consider the ellipse and the system of parallel lines... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale - 1904 - 462 pages
...varies so that B2 — 4 AC approaches zero, how does the center of the locus behave ? 98. Diameters. The locus of the middle points of a system of parallel chords of a curve is called a diameter of the curve. Consider the ellipse 62x2 4- a2?/2 = o2b2 and the system... | |
 | George Albert Wentworth - 1904 - 496 pages
...middle point M will move along MR towards S ; finally, E, M, P, and Q will all coincide at S. 888. DEF. The locus of the middle points of a system of parallel chords in a parabola is called a diameter. The parallel chords are called the ordinates of the diameter. 889.... | |
 | William Meath Baker - 1906 - 363 pages
...of Q, and by (1) this straight line passes through (xv y^) P, which proves the proposition. 145. To find the locus of the middle points of a system of parallel chords. Let OO' be a chord of the system, making an angle 0 with the axis of #, 0 being constant. Let ($!, y±)... | |
 | William Henry Maltbie - 1906 - 156 pages
...special case of the general equation developed in article 62, or it may be found directly by determining the locus of the middle points of a system of parallel chords. If the latter method is adopted, the student should remember that in any locus problem the thing sought... | |
 | Samuel Smith Keller, W. F. Knox - 1908 - 374 pages
...chords. ART. 82. The equation to a diameter oj the ellipse. The diameter it will be remembered, is the locus of the middle points of a system of parallel chords. Analytical Geometry. Let RS be any one of a system of parallel chords of the ellipse ABA'B' (Fig. 44),... | |
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The locus of the middle points of a system of parallel chords in a parabola is called a diameter. 
