...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...

...in two distinct points then the line is called (a) Tangent line (b) Normal (c) Secant (d) None 11. A point moves so that the sum of the squares of its distances from the six faces of a cube is constant. The locus of this point is a (a) Circle (b) Sphere (c) Ellipse...

...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 PQ.R 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...

...; 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...

...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...

...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...

...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...

...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...

...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...