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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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Analytic Geometry

Linnaeus Wayland Dowling, Frederick Eugene Turneaure - Geometry, Analytic - 1914 - 294 pages
...distances from the points (8, 0) and (2, 0) is constantly equal to 2. Find the equation of the locus. 8. A point moves so that the sum of the squares of its distances from (3, 0) and (— 3, 0) is constantly equal to 08. Find the equation of the locus. 9. A circle circumscribes...
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Plane Analytic Geometry: With Introductory Chapters on the Differential Calculus

Maxime B˘cher - Geometry, Analytic - 1915 - 258 pages
...many other cases. We illustrate this by two examples. Example 1. To find the locus of a point which moves so that the sum of the squares of its distances from two fixed points is a constant, which we will call 2 a 2 . Let us take the line connecting the two fixed points as axis...
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Analytic Geometry

Henry Bayard Phillips - Geometry, Analytic - 1915 - 220 pages
...Find its locus. 3. In a triangle ABC, A and В are fixed. Find the locus of C, if A - В = \ т. 4. A point moves So that the sum of the squares of its distances from the three sides of an equilateral triangle is equal to the square of one side of the triangle. Find...
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Plane Analytic Geometry: With Introductory Chapters on the Differential Calculus

Maxime B˘cher - Geometry, Analytic - 1915 - 266 pages
...fixed points. If ź2< c2, there is no locus; that is, it is impossible for a point to be so situated that the sum of the squares of its distances from two fixed points should be less than twice the square of half the segment connecting them. Example 2. To find the locus...
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An Elementary Treatise on Conic Sections by the Methods of Co-ordinate Geometry

Charles Smith - Conic sections - 1916 - 466 pages
...varies as its perpendicular distance from a fixed straight line ; shew that it describes a circle. ix 2. A point moves so that the sum of the squares of its distances from the four sides of a square is constant ; shew that the locus of the point is a circle. 3. The locus...
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Elementary Mathematical Analysis

John Wesley Young, Frank Millett Morgan - Functions - 1917 - 584 pages
...respect to the circles of a pencil pass through a fixed point, unless P is on the line of centers. 13. A point moves so that the sum of the squares of its distances from the sides of a given square is constant. Show that its locus is a circle. 14. A point P moves so that...
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Analytic geometry and calculus

Frederick Shenstone Woods - 1917 - 562 pages
...two fixed points are in a constant ratio k. Show that the locus is a circle except when k = 1. 120. A point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant. Show that the locus is a circle and find its center....
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Elementary Mathematical Analysis

John Wesley Young, Frank Millett Morgan - Functions - 1917 - 588 pages
...that any angle inscribed in a semicircle is a right angle. 6. Prove that the locus of a point which moves so that the sum of the squares of its distances from any number of fixed points is constant is a circle. Find the coordinates of the center of this circle...
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Mathematics for Collegiate Students of Agriculture and General Science

Alfred Monroe Kenyon, William Vernon Lovitt - Mathematics - 1917 - 384 pages
...of its distances from the axes is constant (a2)? 12. Find the equation of the locus of a point which moves so that the sum of the squares of its distances from the three points (5, — 1), (3, 4), (-2, - 3) is always 64. Ans. xl + y2 - 4z = 0. 13. Find the equation...
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Introduction to the Elementary Functions

Raymond Benedict McClenon - Functions - 1918 - 264 pages
...choose the X- and F-axes in a convenient position with reference to the given points or lines. 20. A point moves so that the sum of the squares of its distances from two fixed points is constant. 21. A point moves so that the ratio of its distances from two fixed points is a constant...
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