A point in a plane is such that the sum of its distances from the point (2,2) and (6,2) is 12. Find the locus of the point.

If the distance between the points (1,2,z) and (-1,2,1) is 3, then find z.

A point is such that its distance from the point (3,0) is twice its distance from the point (-3,0). Find the equation of the locus.

Write the distance of the point (2,3,6) from zx-plane.

Find the locus of points which are equidistant from the points (1,2,3) and (3,2,-1).

What is the distance of the point (1, 2, -3) from xy-plane ?

Write the distance of the point (1,1,2) from x-axis.

What is the distance of the point (1,1,1)from the plane y=x?

A point P(x,y) is such that its distance from the fixed point (alpha,0) is equal to its distance from y-axis. Prove that the equation of the locus is given by, y^2 = alpha (2x-alpha) .

Show that the relation R on 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.