...distances from the four sides of a square is constant ; shew that the locus of the point is a circle. 3. The locus of a point, the sum of the squares of whose distances from n fixed points is constant, is a circle. 4. A, B are two fixed points, and P moves so that PA = n ....

...2. Inscribe a square in a given quadrilateral ; and find when the problem is indeterminate. 3. Find the locus of a point, the sum of the squares of whose distances from the sides of a regular polygon is given. 5. If di, dt, di^ dt represent the distances of the centre...

...of the squares of whose distances from any number of points is constant. 10. Derive the equation of the locus of a point the sum of the squares of whose distances from the six faces of a cube is constant. 11. Show that a quadric surface may in general be passed through...

...Length of ± from (2, 4, - 3) on this plane = ^6 + g+l = ~ ^g" = ^Jf (numerically). Example 2. Find the locus of a point the sum of the squares of whose distances from the planes x + y + z = 0, x— y = 0 and x + y — 2z = 0is4. Sol. Let P(.t|, yi, zi) be any point...

...same side of the origin. Hence, the required distance between two planes is -- — = — . 632 2. Find the locus of a point, the sum of the squares of whose distances from the planes x + у + z = 0, x - z = O, x-2y + z = 0is9. Sol. Let the co-ordinates of the point be (a,...

...them a plane in such a way that these planes may intersect in a common line ? 10. Find the equation of the locus of a point the sum of the squares of whose distances from a number of given planes is constant. 11. Substitute " lines " for " planes " in (10). 12. Find the...

...have tb.c = k, so that t = OR 2 OR => OP, OR, OQ are in HP Hence, the result. EXERCISES 1. Prove that the locus of a point, the sum of the squares of whose distances from n given points is constant, is a sphere. 2. Prove that the equation of the sphere circumscribing the...

...If the equations of a system of concentric circles be x2 + y2 = ri2, x2 + y2 = r22, etc. show that the locus of a point the sum of the squares of whose tangents to the circles is constant is a circle. Ex. 27. OAB is a triangle right.angled at O. If P...

...and that they are at right angles if abc p* 2 (a(b + c)/2} = I{a2(b — c)2/n2n«}. 34. Prove that the locus of a point, the sum of the squares of whose normal distances from the ellipsoid is constant (=)fcs), is k-°V (a«_ + 2e2 + 2¿2 + 2c2 = /fe2....