 | Sir Asutosh Mookerjee - 1893 - 197 páginas
...at V. is a fixed straight line bisecting all chords parallel to QQ\ Bel A diameter of any curve is the locus of the middle points of a system of parallel chords drawn in the curve. It has just been proved that the diameters of a parabola are straight lines. It... | |
 | Calvin Frank Allen - 1894 - 232 páginas
...seldom that parabolic curves would be laid out by. instrument. 130. Properties of the Parabola. (a)* The locus of the middle points of a system of parallel' chords of a parabola is a straight line parallel to the axis of the parabola (ie a diameter). (6) The locus of... | |
 | Webster Wells - 1894 - 394 páginas
...parallel chords be drawn in a circle, their middle points lie in the same straight line. 60. What is the locus of the middle points of a system of parallel chords in a circle ? 61. What is the locus of the middle po^^pf a system of chords of given length in a circle... | |
 | Sidney Luxton Loney - 1896 - 447 páginas
...point is, by Art. 205, a y = mx H -- , tt and is therefore parallel to each of the given chords. Hence the locus of the middle points of a system of parallel chords of a parabola is a straight line which is parallel to the axis and meets the curve at a point the tangent... | |
 | 1896 - 154 páginas
...its polar is the same for every circle of the system. How many such points are there ? 6. Shew that the locus of the middle points of a system of parallel chords of a parabola is a straight line parallel to the axis of the parabola. Find also the locus of the middle... | |
 | George Albert Wentworth - 1896 - 68 páginas
...Cor. 2. The perpendicular erected at the middle of a chord bisects the arcs of the chord. 235. Cor. 3. The locus of the middle points of a system of parallel chords is the diameter perpendicular to them. 236. In the same circle, or equal circles, equal chords are... | |
 | Frederick Harold Bailey - 1897 - 392 páginas
...circle is the definition of the diameter for all the conies. Hence the diameter of the parabola is the locus of the middle points of a system of parallel chords. / II Fio. 84. Let y3 = 4px (1) be the parabola, and let m be the common slope of the parallel chords.... | |
 | University of Sydney - 1898 - 548 páginas
...product of the ordinates at its extremities is equal to the square of the latus rectum. 10. Investigate the locus of the middle points of a system of parallel chords of an ellipse, and shew that, if the coordinates of an extremity of a diameter are x'y', those of its... | |
 | Webster Wells - 1898 - 284 páginas
...chords be drawn in a circle, their middle points lie in the same straight line. (§ 162.) 57. What is the locus of the middle points of a system of parallel chords in a circle ? 58. What is the locus of the middle points of a system of chords of given length in a... | |
 | John Henry Tanner, Joseph Allen - 1898 - 458 páginas
...auxiliary circle. 152. Diameters. As already shown in Articles 129 and 139, the definition of a diameter as the locus of the middle points of a system of parallel chords leads directly to its equation. Let TO be the slope of the given system of parallel chords of the ellipse... | |
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The locus of the middle points of a system of parallel chords in a parabola is called a diameter. 
