 Show that the locus of a point such that the sum of the squares of its distances from two fixed points is constant, is a circle.  Solid Geometry - Page 449by George C. Shutts - 1913Full view - About this book
 | Charles Godfrey, Arthur Warry Siddons - Geometry, Modern - 1912 - 190 pages
...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 distances from two fixed points A, B remains constant ; prove that its locus is a circle. Ex. 31. The sum of the squares on the sides... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1912 - 364 pages
...distances from two fixed points is constant. Prove that the locus is a circle. 9. A point moves so that the sum of the squares of its distances from two fixed perpendicular lines is constant. Prove that the locus is a circle. 10. ,A point moves so that the ratio... | |
 | George Clinton Shutts - Geometry - 1913 - 494 pages
...intersect on the surface equal spherical polygons are equal polyhedrals, or equal solid angles. 742. COR. Two trihedrals having a dihedral and the including...from two given points? Discuss all possibilities. 86. Find a point X which is at given distances from two given points and equally distant from two other... | |
 | Linnaeus Wayland Dowling, Frederick Eugene Turneaure - Geometry, Analytic - 1914 - 294 pages
...the points (5, — 3) and (0, 6) and has its center on the line 2.r-3j/-6 = 0. 3. 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. 4. A point moves so that the ratio of its distances... | |
 | Maxime Bôcher - Geometry, Analytic - 1915 - 266 pages
...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 a2. Let us take the line connecting the two fixed points as axis... | |
 | Edward Harrison Askwith - Conic sections - 1917 - 302 pages
...loci of its orthocentre, centroid and nine-points centre are circles. 6. The locus of a point which is such that the sum of the squares of its distances from two given points is constant is a sphere. 7. A', B', G' are three points on the sides BC, CA, AB of a triangle... | |
 | Raymond Benedict McClenon - Functions - 1918 - 264 pages
...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... | |
 | Maria M. Roberts, Julia Trueman Colpitts - Geometry, Analytic - 1918 - 266 pages
...the line 4 z — 3 у — 15 =0. 21. Prove that the following loci are circles: (a) A point moves so that the sum of the squares of its distances from two fixed points is constant. Hint. — When no mention is made of axes or coordinates, it is always advisable tp choose... | |
 | Edwin Schofield Crawley, Henry Brown Evans - Geometry, Analytic - 1918 - 257 pages
...Thus squaring and expanding, it becomes ANALYTIC GEOMETRY [CHAP. II] 3. A point moves in a plane so that the sum of the squares of its distances from two fixed points in the plane is constant. What locus will it describe? The problem is stated without reference to any... | |
 | Eugene Randolph Smith, William Henry Metzler - Geometry, Solid - 1918 - 232 pages
...given plane equidistant from two given coplanar lines outside the plane. 78. Find the locus of a point such that the sum of the squares of its distances from two given fixed points shall be constant. 79. Find the locus of a point such that the difference of the... | |
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