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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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Report of the Committee of Council on Education in Scotland...[without Appendix]

Education - 1901 - 808 pages
...namely, Nos. 1, 2, 3, 4. and one of the alternatives in each of Nos. 5, 6, 7. I. A point moves in a plane so that the sum of the squares of its distances from two given points is constant, prove that its locus is a circle. AHCD is a quadrilateral inscribed in a...
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An Elementary Text-book on the Differential and Integral Calculus

William Holding Echols - Calculus - 1902 - 536 pages
...•= kl, b — y= km, squared and added, give the envelope 9. Find the envelope of a right line when the sum of the squares of its distances from two fixed points is constant, and also when the product of these distances is constant. 10. A point on a right line...
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 384 pages
...Apollonius' theorem to A1 OAC, OBD ; then eliminate OB2. Ex. 114O. In the figure of Ex. 1139, O Ex. 1141. A point moves so that the sum of the squares of its...circle, having for centre the mid-point of AB. Ex. 1 142. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on...
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Notes on Analytical Geometry: An Appendix

Alfred Clement Jones - Geometry - 1903 - 212 pages
...second degree represents straight lines, the equation of the bisectors of the angle between them is 35. A point moves so that the sum of the squares of its distances from two given sides of an equilateral triangle is constant and equal to 2c2. Show that the locus is an ellipse...
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Practical Plane and Solid Geometry for Elementary Students

Joseph Harrison - Geometry - 1903 - 300 pages
...on the circumference. Interpreted, the equation tells us that a circle is the locus of a point which moves so that the sum of the squares of its distances from two perpendicular lines is constant. It can be shown that all curves of determinate form have equations...
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The Elements of Analytic Geometry

Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1904 - 453 pages
...if the "constant difference " be denoted by /<;, we find for the locus 4 ax = k or 4 ax = — k. 13. A point moves so that the sum of the squares of its distances from two fixed points is constant. Prove that the locus is a circle. Hint. Choose axes as in problem 12. 14. A point moves...
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The Elements of Analytic Geometry

Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1904 - 462 pages
...if the "constant difference " be denoted by /:, we find for the locus 4 ax = k or 4 ax = — k. 13. A point moves so that the sum of the squares of its distances from two fixed points is constant. Prove that the locus is a circle. Hint. Choose axes as in problem 12. 14. A point moves...
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The Elements of Plane and Solid Analytic Geometry

Albert Luther Candy - Geometry, Analytic - 1904 - 288 pages
...squares of its distances from the axes is constant (a2) ? •J 13. Find the locus of a point which moves so that the sum of the squares of its distances from the points (a, 0) and (— а, 0) is constant (2 c2). 14. Find the locus of a point which moves so...
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Introduction to Analytic Geometry

Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1905 - 240 pages
...if the "constant difference " be denoted by k, we find for the locus 4 аж = A or 4 ax = — *. 13. A point moves so that the sum of the squares of its distances from two fixed points is constant. Prove that the locus is a circle. Hint. Choose axes as in problem 12. 14. A point moves...
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The Elements of Geometry

Walter Nelson Bush, John Bernard Clarke - Geometry - 1905 - 378 pages
...LG- = 2 LH2 + 2 GJf 2. (Why ?) iff2 + LM2 = 2 it? -(- 2 CJ/2. (Add, and combine terms.) Ex. 43. If L moves so that the sum of the squares of its distances from A, B, and C = a given square ; that is, so that LA2 + LI? + LCT- equals, say i <?2i what is the center...
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