 | Mathematics - 1866 - 426 pages
...to the two circular points at infinity. From this equation it appears at once that the envelope of a chord of a conic which subtends a right angle at a given point ia another conic (which is well known). (4) The equation of the normal to the confocal conic at its... | |
 | Dublin city, univ - 1858 - 264 pages
...equation of a parabola which cuts the axes of co-ordinate in given points. 2. What is the envelope of a chord of a conic which subtends a right angle at a given point on the curve ? 3. Prove that if the line joining the intersection of two tangents and the intersection... | |
 | Norman Macleod Ferrers - Conic sections - 1866 - 236 pages
...the directrix." Now, reciprocate this with respect to any point whatever, and we find that " Every chord of a conic which subtends a right angle at a given point on the curve, passes through a fixed point." Again, take Euc. 1n. 21. This may be expressed under the... | |
 | Joseph Wolstenholme - Mathematics - 1878 - 538 pages
...series. A method which is often the best is exemplified in the following : " To find the envelope of a chord of a conic which subtends a right angle at a given point." Move the origin to the given point, and let the equation of the conic be u = oaf + by' + c + 2/y +... | |
 | Charles Taylor - Mathematics - 1881 - 512 pages
...to equal angles subtended at the reverse origin in the other. [Art. 142 Cor. 2. a. A variable chard of a conic which subtends a right angle at a given...of the latter conic which subtends a right angle at ta envelopes a concentric circle (Ex. 289), of which the obverse is a conic having 0 and the base-line... | |
 | Charles Taylor - Mathematics - 1881 - 486 pages
...the tangent at a given point 0, find the relation between the lengths of ON and PN* 279. If PQ be a chord of a conic which subtends a right angle at a given point 0 on the curve, and MN be the projection of the chord upon the tangent at 0, shew that PM A QN OP*... | |
 | Cambridge Philosophical Society - Mathematics - 1902 - 580 pages
...as a problem in The Ancient and Modern Geometry of Conies, page 122 (1881), thus, " 279. If PQ be a chord of a conic which subtends a right angle at a given point O on the curve, and MN be the projection of the chord upon the tangent at O, shew that PM QN , = &... | |
 | Cambridge Philosophical Society - Mathematics - 1902 - 602 pages
...as a problem in The Ancient and Modern Geometry of Conies, page 122 (1881), thus, " 279. If PQ be a chord of a conic which subtends a right angle at a given point 0 on the curve, and MN be the projection of the chord upon the tangent at 0, shew that PM QN * = a... | |
 | Cambridge Philosophical Society - Science - 1902 - 1132 pages
...as a problem in The Ancient and Modern Geometry of Conies, page 122 (1881), thus, " 279. If PQ be a chord of a conic which subtends a right angle at a given point 0 on the curve, and MN be the projection of the chord upon the tangent at 0, shew that PM QN OQ1 =... | |
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OI/On, and On is constant and na fixed point. 2. Another proof is given as a problem in The Ancient and Modern Geometry of Conies, page 122 (1881), thus, " 279. If PQ be a chord of a conic which subtends a right angle at a given point... 