 | William Walton - Coordinates - 1851 - 446 pages
...ElSmens d' Analyse Geometrique et d' Analyse Algebrique, p. 181. 2. To find the locus of a point such that the sum of the squares of its distances from any number of proposed points may have a given value. Let there be n proposed points (al9 /3J, (a2, /32), (a8, /33),... | |
 | Isaac Todhunter - Geometry - 1855 - 332 pages
...the sides of an equilateral triangle is constant ; shew that the locus of the point is a circle. 13. A point moves so that the sum of the squares of its distances from any given number of fixed points is constant ; shew that the locus is a circle. 14. Shew what the equation... | |
 | Isaac Todhunter - 1855 - 376 pages
...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... | |
 | Isaac Todhunter - Conic sections - 1858 - 334 pages
...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... | |
 | Stephen Parkinson - Dynamics - 1863 - 396 pages
...between consecutive impacts decrease in geometrical progression. 9. A point moves in such a manner that the sum of the squares of its distances from any number of given points in the same plane with it is constant. Prove that if perpendiculars from the points be at any time... | |
 | Thomas Kimber - Mathematics - 1865 - 302 pages
...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 - Coordinates, Trilinear - 1866 - 558 pages
...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 - Geometry, Analytic - 1867 - 276 pages
...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 pages
...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, Peter Guthrie Tait - Quaternions - 1873 - 254 pages
...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... | |
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A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant. 
