 | 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 of the corresponding... | |
 | George Salmon - Conic sections - 1863 - 412 pages
...L'S' = 0. If the point a'/3'y' be on the curve the equation reduces to L'S— 2.Z/P=0. Ex. A chord which subtends a right angle at a given point on the curve, passei through a fixed point (Ex. 2, p. 1 (;.">.). "YVe use ordinary rectangular co-ordinates, and,... | |
 | George Salmon - Conic sections - 1869 - 426 pages
...L'*S-'2LL'P+ US' = 0. If the point a'/Sy be on the curve the equation reduces to L'S— 2LP= 0. Ex. A chord which subtends a right angle at a given point on the curve, passes through a fixed point (Ex. 2, p. 170). We use ordinary rectangular co-ordinates, and, as above, form the equation of 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 - 488 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*... | |
 | Samuel Earnshaw - Differential equations, Partial - 1881 - 602 pages
...correspond to equal angles subtended at the reverse origin in the other. [Art. 142 Cor. 2. a. A variable chord of a conic which subtends a right angle at a given point envelopes a conic having that point for a focus. For if the given point 0 and its polar be taken as... | |
 | 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 point envelopes a conic having that point for a focus. ' For if the given point 0 and its polar be taken... | |
 | Dublin city, univ - 1883 - 510 pages
...normals drawn at corresponding poinis on two concentric and coaxal ellipses. 2 . Find the envelope of a chord of a conic which subtends a right angle at a given point. 3. If a, ft, y, &c., he the roots of the equation x" + pix°-v + pix°-* + . . . + pn = o, find the... | |
 | 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 , = &... | |
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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... 
