 | William Peveril Turnbull - Geometry, Analytic - 1867 - 298 pages
...for all conic sections the last theorem in Art. 101, and prove that the centre of the conic <}> (xy) is the pole of the line at infinity. 36. With a given...equation to the mid-parallel of the lines Ax + By + C, Ax+By + C' (Art. 180). 45. The lines L — pM, L+pM are conjugate diameters of the curve LM= Te. 46.... | |
 | William Henry Besant - Conic sections - 1869 - 304 pages
...Q, R, the diameters parallel to LR, PQ are equal : hence 0 is a point on the curve. 139. PROP. IX. If a rectangular hyperbola circumscribe a triangle, the locus of its centre is the nine-point circle of the triangle. If PQR be the triangle, let L, L' be the points in which an asymptote meets the sides... | |
 | Sir Asutosh Mookerjee - Conic sections - 1893 - 197 pages
...on the curve to the tangent at P. Prove that the circle round CNP bisects PQ. (Apply Ex. 4.) Ex. 8. If a rectangular hyperbola circumscribe a triangle,...the locus of its centre is the nine-point circle. [The diameters to the middle points of the sides are conjugate to the sides respectively.] Ex. 9. The... | |
 | Charlotte Angas Scott - Geometry, Analytic - 1894 - 344 pages
...orthocentre (nine points in all) lie on a circle, called the Nine Points Circle (NPC) of the triangle ; (ii.) If a rectangular hyperbola circumscribe a triangle, the locus of its centre is the NPC Note. All these theorems relate properly not to a triangle 1'fyK, but to a particular configuration... | |
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If a rectangular hyperbola circumscribe a triangle, the locus of its centre is the 