A point moves in such a manner that the sum of the squares of its distances from the origin and the point (2, -3) is always 19. Show that the locus of the moving point is a circle. Find the equation to the locus.

A point movs in such a manner that the sum of the squares of its distances from the points (a,0) and (-a, 0) is 2b^(2). Then the locus of the moving point is-

If the square of distance of a moving point from the point (2,0) is equal to 4 units , then the locus of the moving point is a -

A point moves so that the sum of squares of its distances from the points (1,2) and (-2,1) is always 6 . Then its locus is _

A point moves so that the sum of squares of its distances from the points (1, 2) and (-2, 1) is always 6. Then its locus is

A point moves so that sum of the squares of its distances from the vertices of a triangle is always constant. Prove that the locus of the moving point is a circle whose centre is the centroid of the given triangle.

Find the locus of the point such that the sum of the squares of its distances from the points (2, 4) and (-3, -1) is 30.

A point moves so that the sum of squares of its distances from the points (1, 2) and (-2,1) is always 6. Then its locus is

A point moves so that the sum of squares of its distances from the points (1,2) and (-2,1) is always 6. then its locus is

The point P moves such that the sum of the squares of its distances from two fixed points A(a,0),B(-a,0) is 8a^(2) the locus of P is

A point moves such that the sum of the square of its distances from two fixed straight lines intersecting at angle 2alpha is a constant. Prove that the locus of points is an ellipse