If the sum of squares of distances of a point P from the two poitns (-5,2) and (1,4) is 52, show that the locus of P is a circle. Find its centre and radius.

Show that the points (5, 5),(6, 4),(- 2, 4) and (7, 1) all lie on a circle. Find its equation, centre and radius.

If the sum of the distances of a variable point from two perpendicular lines in a plane is 1, then its locus is :

The sum of the squares of the distances of a moving point from two fixed points (a,0) and (-a ,0) is equal to a constant quantity 2c^2 . Find the equation to its locus.

Find the distance of the point (1,2,3) from the line joining the points (-1,2,5) and (2,3,4).

Show that the relation R in the set A of points in a plane given by R = {(P, Q) : distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related to a point P ne (0, 0) is the circle passing through P with origin as centre.

If two tangents drawn from a point P to the parabola y2 = 4x are at right angles, then the locus of P is

Find the distance between the points P(-2, 4, 1) and Q(1, 2, -5).

The angle between a pair of tangents drawn from a point P to the parabola y^2= 4ax is 45^@ . Show that the locus of the point P is a hyperbola.

Find the equation of the circle with the centre (1/2,1/4) and radius 1/2 .

Find the equation of circle passing through the points : (1, -2), (5, 4) and (10, 5). Also find its centre and radius.