...OP cos oOP) = 0, that is, 2 (A . oP2) = 0, as was to be proved. 1562 (Proposed by FD THOMSON, MA)— Find the locus of the points of contact of tangents...locus for different positions of the given point. Solution by PBOFESSOB CiYLEY; and the PBOPOBEB. Let O be the given point; 1, 2, 3, 4 the vertices of...

...be drawn two real or imaginary tangents to a conic section. 231. To find the equation to the chord of contact of tangents drawn from a given point to a conic section. Let (a', ft, 7') be the given point, and /(a,/9,7)=0 the equation to the conic. Then if (a",...

...respect to a given conic ; the locus of the feet of these perpendiculars is the circular cubic which is the locus of the points of contact of tangents drawn from a fixed point (the pole of the fixed straight line) to the conies confocal with the given conic. The...

...respect to a given conic ; the locus of the feet of these perpendiculars is the circular cubic which is the locus of the points of contact of tangents drawn from a fixed point (the pole of the fixed straight line) to the conies confocal with the given conic. The...

.......................................... 26 7711. (Professor Wolstenholme, MA, Sc.D.)— Prove that (1) the locus of the points of contact of tangents drawn from a given point O to a series of confocal parabolas isacircular cubic, whose equation withO as origin is r = 2« sin...

.......................................... 25 7711. (Professor Wolstenholme, MA, Sc.D.)— Prove that (1) the locus of the points of contact of tangents drawn from a given point 0 to a series of coni'ocal parabolas isacircular cubic, whose equation withO as origin is r = la sin...

...estimated from the ratio (T' : T)2. 7711. (By Professor WOLSTENHOLME, MA, So. D.) — Provethat (1)the locus of the points of contact of tangents drawn from a given point O to a series of confocal parabolas is a circular cubic, whose equation with O as origin is r = 2я...

...that 36 passes through 0. ED. [WJ M].}. [Vol. п. pp. 70—72.] 1562. (Proposed by FD THOMSON, MA) — Find the locus of the points of contact of tangents...locus for different positions of the given point. Solution by PROFESSOR CAYLEY; and the PROPOSER. Let 0 be the given point ; 1, 2, 3, 4 the vertices...

...Distinguish between the cases when the given point is within, on, or without the circumference. 41. Find the locus of the points of contact of tangents drawn from a fixed point to a system of concentric circles. 42. Find the locus of the intersection of straight lines...

...of the bisectors of the angles BAX, YBA. (Take, for the first point, that found when AXJ. AB.) 375. Find the locus of the points of contact of tangents drawn from a fixed point to a system of concentric circles. 376. Two opposite vertices of a given square move on...