If A and B are the points (1,2,3) and (0,-1,2) and P is a point such that `AP^2 - BP^2 = 10`. Find the equation to the locus of P.

A point P is taken on 'L' such that 2/(OP) = 1/(OA) +1/(OB) , then the locus of P is

The line joining the points A (- 3,- 10) and B (- 2, 6) is divided by the point P such that 5 PB = AB. Find the co-ordinates of P.

If A and B be the points (3, 4, 5) and (-1,3, -7), respectively, find the equation of the set of points P such that PA^2 + PB^2 = k^2 , where k is a constant.

If A and B be the points (3,4,5) and (-1,3,-7) respectively, find the equation of the set of point P such that PA^2+PB^2=k^2 , where k is constant.

Show that the points A(2,3,4),B(-1,2,-3) and C(-4,1,-10) are collinear. Find the equations of the line in which they lie.

Show that the points (1,-1,1),(2,3,1),(1,2,3) and (0,-2,3) are coplanar. Find the equation of the plane in which they lie.

Find p if the points (p+1,1), (2p + 1,3) and (2p + 2, 2p) are collinear.

The angle between a pair of tangents from a point P to the circle x^2 + y^2 = 25 is pi/3 . Find the equation of the locus of the point P.

Let P and Q be the points on the line joining A(-2, 5) and B(3, 1) such that AP = PQ=QB . Then, the mid-point of PQ is

If a circle passes through the point (a, b) and cuts the circle x^2+ y^2 = p^2 orthogonally, then the equation of the locus of its centre is :