...satisfied and a fixed plane be drawn perpendicular to each straight line, the locus of a point which moves so that the sum of the squares of its distances from the planes is constant will be a sphere having a fixed centre 0 which is the centre of inertia of equal...

...geometrically, that A Yj and AYa are together equal to the distance of P from the axis. 5. A straight line moves so that the sum of the squares of its distances from the two points A and B at a distance 2a apart is equal to rf2. Prove, either analytically or geometrically,...

...the intersection of AP and BQ is a circle whose centre is in the given circle, and radius is VZR. 85. A point moves so that the sum of the squares of its distances from the four sides of a square is constant; show that the locus of the point is a circle. 30. Show that...

...the radius of which is equal to a. Interpret each of the equations а? + y* = 0 and of — y* = 0. A point moves so that the sum of the squares of its distances from the three angles of a triangle is constant. Prove that it moves along the circumference of a circle....

...vertex. [Take the base and a perpendicular through its centre for axes.] Ans. ж2 + у2 = s2 — m2. 23. A point moves so that the sum of the squares of its distances from the four sides of a square is constant; show that the locus of the point is a circle. 24. Find the...

...straight lines. 9. Inscribe a regular pentagon in a given circle. 10. Find the locus of a point which moves so that the sum of the squares of its distances from four given points is constant. What is the least possible value of this constant. ANSWEES TO THE GEOMETRY...

...4), and (5, - 2) are equal to one another ; find the equation of its locus. Ans. x-3?/ = l. Ex. 2. A point moves so that the sum of the squares of its distances from the two fixed points (a, 0) and ( - a, 0) is constant (2c2) ; find the equation of its locus. Ans....

...of the squares of whose distances from any number of given points is constant, is a sphere. Ex. 3. A point moves so that the sum of the squares of its distances from the six faces of a cube is constant ; shew that its locus is a sphere. Ex. 4. A, B are two fixed points,...

...11. What curve does p = a cos (6 — a) + b cos (d — ft) + c cos (d — y) + . . . represent? 12. A point moves so that the sum of the squares of its distances from the four sides of a rectangle is constant. Show that the locus of the point is a circle. 13. Given...

...distance from the axis of x is half its distance from the origin ; find the equation of its locus. 20. A point moves so that the sum of the squares of its distances from the two fixed points (a, 0) and ( — a, 0) is the constant 2k2; find the equation of its locus. 21....