 | Charles Smith - Conic sections - 1890 - 372 pages
...on the directrix the line joining the points of contact will pass through the focus. 102. The locuA of the middle points of a system of parallel chords of a parabola is a straight line parallel to the axis of the parabola. The equation of the straight line joining the two points (x',... | |
 | Edward Wyllys Hyde - Ausdehnungslehre - 1890 - 288 pages
...must put in (327) x = 1, and £ for q2, thus obtaining y = — | — — (ool) 106. Diameters. To find the locus of the middle points of a system of parallel chords of the locus of (325). In (331) let ql be on the curve, so that we have q1\^>ql = 0 ; then y=_ gl^£.... | |
 | Charles Smith - Conic sections - 1890 - 372 pages
...; 1 q •••0<T c <»>• From (i) and (ii) we see that _ L _ . OP+ OR" OQ • 182. To find ike 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 a(x- a,') (x - x"} +h{(x-... | |
 | George Albert Wentworth - Geometry - 1892 - 468 pages
...the line RM is the locus of the middle points of all chords drawn parallel to the tangent at S. 830. 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 ordinatcs of the diameter. 831.... | |
 | Euclid - Geometry - 1892 - 460 pages
...line joining the middle points of two parallel chords of 1i 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... | |
 | John Casey - Geometry, Analytic - 1893 - 610 pages
...semidiameters differ by -. 6. Apply the method of the eccentric angle to the proof of the proposition that the locus of the middle points of a system of parallel chorda is a right line. 6. Find the equation of the hyperbola, referred to a pair of conjugate diameters... | |
 | Sir Asutosh Mookerjee - Conic sections - 1893 - 197 pages
...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 - Railroads - 1894 - 232 pages
...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 the intersection of pairs of... | |
 | Webster Wells - Geometry - 1894 - 394 pages
...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... | |
 | 1896 - 154 pages
...that 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 points of chords of a parabola... | |
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The locus of the middle points of a system of parallel chords in a parabola is called a diameter. 
