 | 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... | |
 | 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 Peveril Turnbull - Geometry, Analytic - 1867 - 298 pages
...distances from two other points a^, xtyt. 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 of the point.... | |
 | W. P. Turnbull - Geometry, Analytic - 1867 - 276 pages
...given that the locus of P is a circle, find geometrically the circle's position and magnitude. 21. A point moves so that the sum of the squares of its distances from any number of given points is constant. Prove that the locus of this point is a circle. 22. Find the... | |
 | 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... | |
 | Benjamin Williamson - Calculus, Differential - 1872 - 372 pages
...difficulty in giving the geometrical interpretation of the preceding result. i49. To find a point such that the sum of the squares of its distances from n given points shall be a Minimum. — Let («, b, с), (а, b', с), &с., be the co-ordinates of the given... | |
 | 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... | |
 | Philip Kelland - 1873 - 248 pages
...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... | |
 | Benjamin Williamson - Calculus - 1873 - 394 pages
...difficulty in giving the geometrical interpretation of the preceding result. 102. To find a point such that the sum of the squares of its distances from n given points shall be a Minimum. — Let (a, b, c), (a', b', c'), &c. be the co-ordinates of the given points... | |
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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. 
