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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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Elementary Analysis

Percey Franklyn Smith, William Anthony Granville - Calculus - 1910 - 248 pages
...and if the "constant difference" be denoted by k, we find for the locus 4 ax = k or 4 ax = — k. 11. 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 10. 12. A point moves...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...intersection points of the bisectors of its interior base angles. 20. Find the locus of a point P such that the sum of the squares of its distances from two fixed points is constant. + 2 REVIEW AH I) FURTHER APPLICATIONS. 21. Find the locus of a point P such that the ratio...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 304 pages
...intersection points of the bisectors of its interior base angles. 2O. Find the locus of a point P such that the sum of the squares of its distances from two fixed points is constant. REVIEW AND FURTHER APPLICATIONS. 21. Find the locus of a point P such that the ratio of...
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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...to be the locus of a point which satisfies a given condition? Show that the locus of a point which moves so that the sum of the squares of its distances from two fixed points is constant is a circle whose centre is the middle point of the two fixed points. JUNE, 1905 1. What...
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Modern Geometry

Charles Godfrey, Arthur Warry Siddons - Geometry, Modern - 1912 - 190 pages
...generalized theorem, of which Apollonius' theorem is a particular case. Also compare Ex. 27.) Ex. 0O. 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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New Analytic Geometry

Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1912 - 364 pages
...revolution when the ratio is less than unity, and a hyperboloid of revolution when greater than unity. 7. A point moves so that the sum of the squares of its distances from two intersecting perpendicular lines in space is constant. Prove that the locus is an ellipsoid of revolution....
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New Analytic Geometry

Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1912 - 364 pages
...following loci are circles, and find the radius and the coordinates of the center in each case : (a) A point moves so that the sum of the squares of its distances from (3, 0) and (- 3, 0) always equals 68. Ana. x2 + j/2 = 25. (b) A point moves so that its distances from...
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Calendar, Part 3

University of Calcutta - 1912 - 746 pages
...may be collinear. 2. Define a circle. From your definition obtain the general equation of the circle. A point moves so that the sum of the squares of its distances from the four sides of a square is constant; prove that the locus is a circle. Determine the centre and...
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1912 - 392 pages
...C'D-DE, 4. How many degrees in arc B'E? In arc C'D? Why? 1, What is the locus of a point in space such that the sum of the squares of its distances from two fixed points equals the square of the distance between the two fixed points? PROPOSITION XXII. 737. THEOBEM. Two...
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Solid Geometry

George C. Shutts - 1913 - 212 pages
...symmetrical and equal. SUG. Use Prop. 740, and 720. 83. What is the locus of a point in space such that the sum of the squares of its distances from two fixed points equals the square of the distance between the two fixed points? 84. Construct a plane tangent to a...
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