 | W. P. Turnbull - Geometry, Analytic - 1867 - 276 pages
...the same y b This equation is satisfied by the co-ordinates of F. That is, F lies on the line a/3. (3) A point moves so that the difference of the squares...Let OA = a, and let xy be the moving point P. Then PA 2 =(xa) 2 + y z , and P5 2 = (x + a) If then PB Z - PA Z = a constant quantity F, ? = A) 2 and x... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...from two given points is equal to a given constant, k*. (III. 62.) 175. Find the locus of a point such that the difference of the squares of its distances from two given points is equal to a given constant k-. (III. 62. ) 176. If A, B and C are three given points in the same straight... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...distances from two given points is equal to a given constant. 307. Locus of a point in a given plane such that the difference of the squares of its distances from two given points is equal to -a given constant. 308. A straight line of a given length moves so that its extremities are... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...sphere whose diameter is the distance between the points. THEOREM VII. 14. The locus of a point such that the difference of the squares of its distances from two given points is equal to the square of the distance between the points is a line through either of the points perpendicular... | |
 | James Maurice Wilson - 1878 - 450 pages
...angles at the base, construct the triangle. 5. Find the locus of 'a point which moves so that the sum of the squares of its distances from two given points is constant. We subjoin a few problems and theorems as miscellaneous exercises in the Geometry of angles, lines,... | |
 | George Albert Wentworth - 1879 - 196 pages
...parts whose squares shall be to each other as two given lines. Ex. 368. Find the locus of a point which moves so that the difference of the squares of its distances from two fixed points is always equal to a given square. Ex. 369. Construct on the diagonal of a given rectangle... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...sphere whose diameter is the distance between the points. THEOREM VII. 14i The locus of a point such that the difference of the squares of its distances from two given points is equal to the square of the distance between the points is a line through either of the points perpendicular... | |
 | Charles Scott Venable - 1881 - 380 pages
...the problem if the four points are all in the same plane. 7. Find upon a straight line a point such that the difference of the squares of its distances from two given points is a given square. 8. Through a given straight line draw a plane which shall be parallel to a given straight... | |
 | Charles Smith - Conic sections - 1883 - 388 pages
...points (a, 0) and ( - a, 0) is constant (2c2) ; find the equation of its locus. Ans. z2 + ?/2=c2-a2. Ex. 3. A point moves so that the difference of the squares of its distances from the two fixed points (a, 0) and ( - a, 0) is constant (cs) ; find the equation of its locus. Ans. 4ox=±cs.... | |
 | George Albert Wentworth - 1884 - 264 pages
...V — 100. , a constant quantity. 0, -• B Fig. 71. Fig. 72. 10. To find the locus of a point such that the difference of the squares of its distances from two given points A, B is constant. The locus consists of two straight lines perpendicular to the line AB. If P (Fig.... | |
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A point moves so that the difference of the squares of its distances from (3, 0) and (0, — 2) is always equal to 8. 
