 | 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... | |
 | University of Sydney - 1898 - 548 páginas
...equation in Cartesian co-ordinates. Shew that it is perpendicular to the line joining the centres. 3. Find the locus of the middle points of a system of parallel chords of a parabola. Obtain also the equation to the locus of the middle points of all chords of a parabola... | |
 | William James Milne - 1899 - 258 páginas
...383. Find the locus of the center of a circle tangent to each of two intersecting lines. Ex. 384. Find the locus of the middle points of a system of parallel chords drawn in a circle. Ex. 385. Find the locus of the middle points of equal chords of a given circle.... | |
 | William James Milne - 1899 - 326 páginas
...bisectors of the two pairs of vertical A formed by the lines constitute the required locus. Ex. 384. Find the locus of the middle points of a system of parallel chords drawn in a circle. Solution. Since, Ex. 187, a diameter that bisects one of the chords is perpendicular... | |
 | George Albert Wentworth - 1899 - 500 páginas
...middle point M will move along MR towards S; finally, R, 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.... | |
 | George Albert Wentworth - 1899 - 248 páginas
...middle point M will move along MR towards S ; finally, -E, M, P, and Q will all coincide at S. 888. DBF. 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.... | |
 | Charles Austin Hobbs - 1899 - 266 páginas
...locus of the centre of a circle whose circumference passes through two given points. Ex. 251. Find the locus of the middle points of a system of parallel chords drawn in a circle. Ex. 252. Through a given point within a given circle to draw a chord which shall... | |
 | Charles Hamilton Ashton - 1902 - 306 páginas
...point of contact from the centre. CHAPTER XI DIAMETERS 79. The diameter of a conic may be defined as the locus of the middle points of a system of parallel chords. The method of finding this locus has already been illustrated for the circle on page 94. We shall repeat... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 330 páginas
...line joining the middle points of two parallel chords of a circle passes through the centre. I1. 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... | |
 | Josiah Willard Gibbs, Edwin Bidwell Wilson - 1901 - 468 páginas
...:j~- fy & r.0.r = -,+ |s+^ = l (9) a3 b3 c2 or N • 0-1 • N = a2 uz + bz v* + c2 w* = 1. (10) 138.] The locus of the middle points of a system of parallel chords in an ellipsoid is a plane. This plane is called the diametral plane conjugate with the system of chords.... | |
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To prove 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. 
