 | 1910 - 322 pages
...double of F, and if the bisector of the angle G meets FH in K, prove that FK = GK = GH. (b) 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, having for centre the midpoint... | |
 | Percey Franklyn Smith, William Anthony Granville - Calculus - 1910 - 250 pages
..."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.... | |
 | Norman Colman Riggs - Geometry, Analytic - 1910 - 328 pages
...circle with center at the origin and radius r. 12. A circle tangent to both axes and radius r. 14. The locus of a point which moves so that the sum of its distances from (0, 3) and (0, — 3) is 8. 15. The locus of a point which moves so that the difference... | |
 | Geometry, Plane - 1911 - 192 pages
...square. 7. When is a circle said 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.... | |
 | John Henry Tanner, Joseph Allen - Geometry, Analytic - 1911 - 330 pages
...4 times its ordinate. Find the equation of its locus and trace the curve. 32. Find the equation of the locus of a point which moves so that the sum of its distances from the points (~1, 3) and (7, 3) is always 10. Trace and discuss the curve. 33. Find... | |
 | Norman Colman Riggs - Geometry, Analytic - 1911 - 330 pages
...tangent to both axes and radius r. 13. A circle tangent to the ?/-axis at the origin and radius r. 14. The locus of a point which moves so that the sum of its distances from (0, 3) and (0, - 3) is 8. 15. The locus of a point which moves so that the difference... | |
 | Charles Godfrey, Arthur Warry Siddons - Geometry, Modern - 1912 - 190 pages
...construction. ,\ in that case P, Q, R, S are concyclic. Ex. 344. If ABC is an equilateral triangle, find the locus of a point which moves so that the sum of its distances from B and C is equal to its distance from A. Several theorems in trigonometry may be... | |
 | Horatio Scott Carslaw - Calculus - 1912 - 174 pages
...on the ellipse — + rs = l- Prove that Ct" O SP=a + exl and S'P=a-exl> and deduce that the curve is the locus of a point which moves so that the sum of its distances from two fixed points is constant. 4. The tangent at P meets the major axis in T, and... | |
 | Percey Franklyn Smith, Arthur Sullivan Gale - Geometry, Analytic - 1912 - 364 pages
...squares of its 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... | |
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Find the locus of a point, the distances of which from two given straight lines have a fixed ratio. 143. Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from... 
