...y respectively. Show that the locus of its centre of the circle is дс* - уг = аг - Ьг. 25. A point moves so that the sum of the squares of its distances from the three points (x\, >¡), (ль, уг) and (дез, >з) is constant (= <f). Prove that the locus...

...the opposite side is the directrix, and the original position of the moving corner the focus. Ex. 52. A point moves so that the sum of the squares of its distances from two intersecting straight lines is constant. Prove that its locus is an ellipse and find its eccentricity...

...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...

...; 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...

...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...

...circles — and find the angle between those diameters of these which pass through the origin. 14. A point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant, = fc2, say. Show that the locus of the point is a...

...Apollonius' theorem become if the vertex moves down (i) on to the base, (ii) on to the base produced? Ex. 64. A point moves so that the sum of the squares of its distances from two fixed points A, B remains constant; prove that its loons is a circle having for centre the mid-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...

...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...