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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. "
Theoretical Geometry: Based on the Various Geometry Books by Godfrey and Siddons - Page 70
by Arthur Warry Siddons, Reginald Thomas Hughes - 1926 - 173 pages
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modern geometry

Ray C. Jurgensen, Alfred J. Donnelly, Mary P. Dolciani - Geometry - 1963 - 198 pages
...generalized theorem, of which Apollonius' theorem is a particular case. Also compare Ex. 27.) Ex. 3O. A point moves so that the sum of the squares of its...remains constant ; prove that its locus is a circle. Ex. 31. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on...
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Practical Geometry

Thomas Tate (Mathematical Master, Training College, Battersea.) - 1860 - 404 pages
...(i) on to the base, (ii) on to the base produced ? tEx. 2 14. A point moves so that the sum of tbe squares of its distances from two fixed points A,...is a circle having for centre the mid.point of AB. I CIRCLE. ARCS AND CHORDS. tEx. 215. PQ, PR are a chord and a diameter meeting at a point P on the...
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Paractical Geometry Based on the Various Geometry Books by Godfrey and Siddons

480 pages
...Apollonius' theorem become if the vertex moves down (i) on to the base, (ii) on to the base produced? Ex. 64. A point moves so that the sum of the squares of its...fixed points A, B remains constant; prove that its loons is a circle having for centre the mid-point of AB. Ex. 66. The base AD of a triangle OAD is trisected...
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Calendar

University of St. Andrews - 1905 - 682 pages
...Find an expression for the distance between two points in terms of their co-ordinates. The point P moves so that the sum of the squares of its distances from two fixed points A and B, is constant ; prove that its locus is a circle whose centre is midway between A and B. 9. Find...
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S.Chand’S Mathematics For Class XI

H.K. Dass & Rama Verma - Mathematics - 1032 pages
...Show that the points (0, 4, 1), (2, 3, -1), (4, 5, 0), (2, 6, 2) are the vertices of a square. 15. A point moves so that the sum of the squares of its distances from the six faces of a cube is constant. Show that its locus is a sphere. 16. Find the locus of the point...
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anaytical geometry a first course

394 pages
...distances from the equal sides. Find its locus. [Take base y = 0 and sides of gradient ni.] Ex. 30. A point moves so that the sum of the squares of its distances from the sides of a triangle is fixed. Find its locus. [Take base ;/..=<) and sides of gradients i, and...
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Cartesian of the Plane

352 pages
...lines meet, and the area of the triangle whose corners are (0, 0), (0, 8) and this meeting-point. 6. A point moves so that the sum of the squares of its distances from the three points (0, 4), (0, - 4), (6, 3) is 362. Find the equation of its locus. Show that this locus...
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Calendar

University of St. Andrews - 1898 - 608 pages
...circles — and find the angle between those diameters of these which pass through the origin. 14. A point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant, = fc2, say. Show that the locus of the point is a...
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Textbook Of Engineering Mathematics

Debashis Dutta - 2006 - 954 pages
...in two distinct points then the line is called (a) Tangent line (b) Normal (c) Secant (d) None 11. A point moves so that the sum of the squares of its distances from the six faces of a cube is constant. The locus of this point is a (a) Circle (b) Sphere (c) Ellipse...
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A Textbook Of Mathematics

B.K. Dev Sarma - 2003 - 676 pages
...y respectively. Show that the locus of its centre of the circle is дс* - уг = аг - Ьг. 25. A point moves so that the sum of the squares of its distances from the three points (x\, >), (ль, уг) and (дез, >з) is constant (= <f). Prove that the locus...
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