...middle point M will move along MR towards S; finally, R, 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....

...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...

...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....

...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...

...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...

...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...

...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....

...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...

...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 ($!,...

...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),...