...term, the plane passes through the origin, that is, the centre of the quadric. Hence: THEOREM. VI. The locus of the middle points of a system of parallel chords of a quadric is a plane through the centre. Def. A plane through the centre of a quadric is called...

...chord whose length is constant. THE CIRCLE. SUPPLEMENTARY PROPOSITIONS. 68. A Diameter of a curve is the locus of the middle points of a system of parallel chords. The chords which any diameter bisects are called the Chords of that diameter. 69. To find the equation...

...circle Hence or otherwise find the condition that this circle may touch the axis of x. 8. Prove that the locus of the middle points of a system of parallel chords of a parabola is a straight line, and shew that the tangent at the point where this straight line meets...

...circle, find the locus of the extremities of the radii produced. SUPPLEMENTAKY PROPOSITIONS. 76. To find the locus of the middle points of a system of parallel chords in the circle a? -f- y2 = i3. D Fig. 29. Let the equation of any one of the chords (Fig. 29) be y =...

...ж' + -Ihxy -y* + 2gx + 2fy+c = 0 cuts the rectangular co-ordinate axes, is equal to the circle 49. Find the locus of the middle points of a system of parallel chords, drawn between an hyperbola and the conjugate hyperbola. 60. If, in two concentric hyperbolas, whose...

...; and the tangent at either end of the straight line is parallel to the chords. Def. of diameter as the locus of the middle points of a system of parallel chords. NOTE. — The word diameter is frequently used to denote the length of the portion of this straight...

...points. EXERCISES ON THE CHORDS OF CIRCLES. For examples on the intersections of loci, see Art. 20. Find the locus of the middle points of a system of parallel chords for the circle : 1. a? + y* = r>, for chords making 45° with the axis of X. Ans. y = — x. 2. (x...

...we 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^£....

...The 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...

...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....