...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...

...— 0. 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 —...

...lines at right angles to each other, prove that If the plane, I x + my + nz = o, cut the cone, 48. Find the locus of the middle points of a system of parallel chords of a central conicoid. Prove that the sum of the squares of the projections of any three conjugate...

...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....

...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...

...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....

...point perpendicular to the axis, prove that PN: 2AS-TN : PN 87. By means of the last example prove that the locus of the middle points of a system of parallel straight lines is a straight line parallel to the axis. 88. A chord PP' of a parabola is normal to...

...point perpendicular to the axis, prove that PN : 2AS::TN : PN 87. By means of the last example prove that the locus of the middle points of a system of parallel straight lines is a straight line parallel to the axis. 88. A chord PP' of a parabola is normal to...