...- 4)2 = 52 9 + z2-%z+ 16-25 = 0 or x or x which is the required equation of the sphere. Example 2. 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. Sol. Take the centre of the...

...between (1) and (2), ie, x (x - a) + у (у - b) + z (z - c) = 0. => x2 + y2. + z2 - ax - by - cz = 0. 3. 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. (Kumaon, 2003) Sol. Take the...

...axes through an angle # = tan~'j 11. Find the equation to a circle referred to any rectangular axes. A point moves so that the sum of the squares of its distances from any number of fixed points is constant : show that the locus is a circle. 12. Find the equation to the straight line...

...the squares of its distances from three fixed points is constant, ami the position of a point such that the sum of the squares of its distances from any number of given points is a minimum. 3. AP, BO, OR are the altitudes of a triangle ABC : prove that the orthocentre of the triangle...

...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...

...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...

...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...

...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...

...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...