If A and B are respectively the points (-1,6) and (5,4), find the point P such that |PA| = |PB| and area `triangle PAB` = 10 units.

If the coordinates of two points A and B are (3,\ 4) and (5,\ -2) respectively. Find the coordinates of any point P , if PA = PB and area of PAB = 10 sq. units.

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 are the points (3, 4, 5) and (-1, 3,-7) respectively then theset of points Psuch that PA ^(2) + PB ^(2) = K ^(2), where K is a constant lie on a proper sphere if:

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.

The locus of the moving point P such that 2PA=3PB , where A is (0,0) and B is (4,-3), is

A, B, C are respectively the points (1,2), (4, 2), (4, 5). If T_(1), T_(2) are the points of trisection of the line segment BC, the area of the Triangle A T_(1) T_(2) is

Consider A(2,3,4),B(4,3,2) and C(5,2,-1) be any three points. Find the area of triangle ABC.

The co-ordinates of two points A and B are (-1, 4) and (5, 1) respectively. Find the co-ordinates of the point P, which lies on extended time AB such that it is three times as far from B as from A.