 | 1850 - 638 pages
...which we have, therefore, to resolve the geometrical problem (a very elementary one) — ' to find a point such that ' the sum of the squares of its distances from a certain number ' of given points shall be a minimum,' — a problem which is, in effect, identical... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...equal to a given line. The same, except the difference of the sides equal to a given line. 35. To find a point such that the sum of the squares of its distances from two given points shall be equal to a given square. D PROBLEMS. PROBLEM I.* To bisect a given line AB.... | |
 | Isaac Todhunter - Geometry - 1855 - 332 pages
...axes, and 0 being the angle ACP. If an ordinate to P meet QQ' in R, the locus of R is an ellipse. 16. The locus of a point such that the sum of the squares of the perpendiculars drawn from it to the sides of a given triangle shall be constant, is an ellipse... | |
 | Isaac Todhunter - 1855 - 376 pages
...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 moves so that... | |
 | Isaac Todhunter - Conic sections - 1858 - 334 pages
...axes, and 0 being the angle ACP. If an ordinate to P meet QQ' in R, the locus of R is an ellipse. 16. The locus of a point such that the sum of the squares of the perpendiculars drawn from it to the sides of a given triangle shall be constant, is an ellipse... | |
 | 1864 - 96 pages
...is the focus. Prove that the tangents at the vertices of the paraholas thus descrihee intersect in a point, such that the sum of the squares of its distances from the four given points is equal to the square of the diameter of the circle. Solution hy the PROPOSER. Let... | |
 | Mathematics - 1864 - 96 pages
...is the focus. Prove that the tangents at the vertices of the parabolas thus described intersect in a point, such that the sum of the squares of its distances from the four given points is equal to the square of the diameter of the circle 34 1435. Show how to find the... | |
 | Robert Potts - 1865 - 528 pages
...three planes intersect each other at right angles, so that the planes pass through a fixed point ; find the locus of a point, such that the sum of the squares on its distances from the three planes may be constant for all points in the locus. 74. Describe a... | |
 | W. P. Turnbull - Geometry, Analytic - 1867 - 276 pages
...equation to the tangent to the circle 3? + 2/ 2 + 2a?y cos co = c 2 at the point x'y. 19. A point moves so that the sum of the squares of its distances from the sides of a square is constant. Find the locus of this point. Shew that the position of the locus does not depend... | |
 | James Maurice Wilson - Geometry - 1868 - 132 pages
...triangle ABC. 40. Find the locus of the vertices of triangles of equal area upon the same base. 41. Find the locus of a point, such that the sum of the squares on its distances from two given points is equal to the square on the distance between the two points.... | |
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Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points. 
