If A and B be the points `(3,4,5) and (-1,3,-7)` respectively, find the locus of P such that `PA ^(2) + PB ^(2) = k ^(2).`

If A,B are the points ( -2,2,3),(13,-3,13) respectively , find the locus of P such that 3|PA| = 2|PB|

If A(3,4,1) and B(-1,2,3) are two points, then find the locus of a moving point P such that PA^(2)+PB^(2)=2k^(2) .

If A and B are two points having coordinates (-2,\ -2) and (2,\ 4) respectively, find the coordinates of P such that A P=3/7A B .

If A and B are (1,\ 4) and (5,\ 2) respectively, find the coordinates of P when A P//B P=3//4 .

If A and B are (-2,\ -2)\ a n d\ (2,\ -4) , respectively, find the coordinates of P such that A P=3/7A B and P lies on the line segment AB.

If A and B are (2,""2)" "a n d" "(2,""4) , respectively, find the coordinates of P such that A P=3/7 A B and P lies on the line segment AB.

Point A and B have co-ordinates (7, -3) and (1,9) respectively. Find : the value of 'p' if (-2, p) lies on it.

A point P(x ,y ,z) is such that 3P A=2P B , where Aa n dB are the point (1,3,4)a n d(1,-2,-1), irrespectivley. Find the equation to the locus of the point P and verify that the locus is a sphere.

If the distance from P to the points (5,-4) (7,6) are in the ratio 2 :3 , then find the locus of P.

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 triangle PAB is 10.