...assume the form where B and C' have the same or opposite signs according as B and C have. 82. To find the locus of the middle points of a system of parallel chords in any quadric. Let the equation of the surface be Ay? + By' + <7z 2 + 2A'yz + ZB'zx + 2 Gxy + 2A"x+2B"y...

...in P, and the normal at P meet the axis in N, prove that MN is equal to the latus rectum. 13. Find the locus of the middle points of a system of parallel chords in an ellipse. Additional Questions. A. Find the general term in the expansion of Find the coefficient...

...Purser referred to for this article. Conjugate Diameters. 268. DBF. A diametral plane of a conicoid is the locus of the middle points of a system of parallel chords. 269. To find the diametral plane corresponding to a given series of parallel chords in a given central...

...3. To find the equation of that chord of a conic which is bisected at the origin; and to show that the locus of the middle points of a system of parallel chords is a right line. 4. The general equation of the tangents to a conic from a point (x1 y') being U' U...

...an equilateral triangle is constant. Sliaw that the locus of the point it a circle. Ex. 13. To find the locus of the middle points of a system of parallel chords in a circle. The locua is a straight line through the centre perpendicular to the chords. Ex. 1 4....

...meet CP in L, shew that PL 2ab a + CD being the semi-diameter conjugate to CP. 8. Find the equation of the locus of the middle points of a system of parallel chords of the hyperbola xy=£. 9. In the conic - = 1 + e cos 0, find the equation of the tangent at any point....

...Rectum is the focal chord, or chord through the focus, at right angles to the axis. 7. A Diameter is the locus of the middle points of a system of parallel chords: it will be proved that the diameters of conics are straight lines. One diameter is said to be conjugate...

...through two given points. (Two solutions. In what case only one ? In what case no solution ?) It. Find the locus of the middle points of a system of parallel chords. 12. Through a given point within a circle draw a chord which is bisected at this point. § 184. Let...

...angles to the axis Other uses of these terms will be noticed in the course of the work. A Diameter is the locus of the middle points of a system of parallel chords. It will be shewn that the diameters of conies are straight lines. The points in which diameters and...

...angles to the axis Other uses of these terms will be noticed in the coarse of the work. A Diameter is the locus of the middle points of a system of parallel chords. It will be shewn that the diameters of conies are straight lines. The points in which diameters and...