...generalized theorem, of which Apollonius' theorem is a particular case. Also compare Ex. 27.) Ex. 3O. 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...

...side PR of an isosceles A PQR is produced to S so that RS = PR: prove that QS2=2QR2+PR2. tEx. 849. 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 mid-point...

...lines meet, and the area of the triangle whose corners are (0, 0), (0, 8) and this meeting-point. 6. A point moves so that the sum of the squares of its distances from the three points (0, 4), (0, - 4), (6, 3) is 362. Find the equation of its locus. Show that this locus...

...Show that the points (0, 4, 1), (2, 3, -1), (4, 5, 0), (2, 6, 2) are the vertices of a square. 15. A point moves so that the sum of the squares of its distances from the six faces of a cube is constant. Show that its locus is a sphere. 16. Find the locus of the point...

...described; through X a line is drawn cutting the circle at R, S. Show that XR2 + RY2 = XS2 + S Y2. 12. 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 mid-point...

...; then eliminate OB2.) tEx. 1140. In the figure of Ex. 1139, OA' + OD2=OB2 + OC2 + 4BC2. |Ex. 1141. 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 mid-point...

...Find an expression for the distance between two points in terms of their co-ordinates. The point P moves so that the sum of the squares of its distances from two fixed points A and B, is constant ; prove that its locus is a circle whose centre is midway between...

...hypercone from the origin. Exercises 1. Let A and B be two given points of .F.space. A variable point X moves so that the sum of the squares of its distances from A and B is unity. Show that the locus of X does not exist if (A - B)2 > 2, and that if (A - B)2 < 2...

...to its distance from the line l/ix + 3 = 0. 24. Determine the equation of the locus of a point which moves so that the sum of the squares of its distances from the points Q(4, 2) and R(2, - 4) = 5. 16. CIRCLE 16.1 CIRCLE GEOMETRY Topics: 16.1.1 Introduction 16.1.2...

...the required locus. Solution i 378 ISC MATHEMATICS • Example 5 : Find the locus of a point which moves so that the sum of the squares of its distances from the two points (1,0) and (-1, 0) is 10. Solution Let A and B be the points (1,0) and (- 1,0). Let P...