| Isaac Todhunter - 1858 - 334 páginas
...from it on these n lines is constant ; find the conditions that the locus of P may be a circle. 31. A point moves so that the sum of the squares of its distances from the sides of a regular polygon is constant; shew that the locus of the point is a circle. 32. A line... | |
| Thomas Kimber - 1865 - 302 páginas
...the radius of which is equal to a. Interpret each of the equations я? + y* = 0 and x* — y* = 0. A point moves so that the sum of the squares of its distances from the three angles of a triangle is constant. Prove that it moves along the circumference of a circle.... | |
| William Allen Whitworth - 1866 - 558 páginas
...right lines, the polar of any point whatever passes through the intersection of the right lines. (148) A point moves so that the sum of the squares of its distances from n given straight lines is constant. Shew that it will describe a conic section. (149) If all but one... | |
| W. P. Turnbull - 1867 - 276 páginas
...from two other points # 3 y 3 , x 4 y 4 . Prove that the locus of the point is the straight line 32. A point moves so that the sum of the squares of its distances from n given points = the sum of the squares of its distances from n other given points. Find the locus... | |
| James Maurice Wilson - 1869 - 260 páginas
...intersect in the line which joins the middle point of the diagonals. 77. The locus of a point which moves so that the sum of the squares of its distances from three given points is constant is a circle. BOOK II. THE CIRCLE. INTRODUCTION. Def. 1. IF a point moves... | |
| Philip Kelland - 1873 - 248 páginas
...given sphere : a point Q is taken in OP so that OP.OQ = k'. Prove that the locus of Q is a sphere. 11. A point moves so that the sum of the squares of its distances from a number of given points is constant. Prove that its locus is a sphere. 12. A sphere touches each of... | |
| Philip Kelland, Peter Guthrie Tait - 1873 - 254 páginas
...constant. Prove that its locus is either a plane or a. sphere. EX. 11.] ADDITIONAL EXAMPLES. 89 11. A point moves so that the sum of the squares of its distances from a number of given points is constant. Prove that its locus is a sphere. 12. A sphere touches each of... | |
| James White - 1878 - 160 páginas
...examples the base is taken as axis of x, and a perpendicular through its middle point as axis of y. 13. A point moves so that the sum of the squares of its distances from the sides of a square, or from the angles of a square, are constant; shew that in both cases the loci... | |
| J. G - 1878 - 408 páginas
...from the four sides of a square is constant. Show that the locus of the point ii a circle. Ex. 12. A point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant. Sliaw that the locus of the point it a circle. Ex.... | |
| 1878 - 228 páginas
...geometrically, that A Yj and AYa are together equal to the distance of P from the axis. 5. A straight line moves so that the sum of the squares of its distances from the two points A and B at a distance 2a apart is equal to rf2. Prove, either analytically or geometrically,... | |
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