`A(1,2),B(2,- 3),C(-2,3)` are 3 points. A point P moves such that `PA^(2)+PB^(2)=2PC^(2)` . Show that the equation to the locus of P is 7 x - 7y + 4 = 0 .

A(2, 0) and B(4, 0) are two given points. A point P moves so that PA^(2)+PB^(2)=10 . Find the locus of P.

A(2,3) , B (1,5), C(-1,2) are the three points . If P is a point such that PA^(2)+PB^(2)=2PC^2 , then find locus of P.

A (c,0) and B (-c,0) are two points . If P is a point such that PA + PB = 2a where 0 lt c lt a, then find the locus of P.

The coordinates of the point A and B are (a,0) and (-a ,0), respectively. If a point P moves so that P A^2-P B^2=2k^2, when k is constant, then find the equation to the locus of the point P .

A and B are two given points whose coordinates are (-5, 3) and (2, 4) respectively. A point P moves in such a manner that PA : PB = 3:2 . Find the equation to the locus traced out by P .

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) .

The coordinates of the point A and B are (a,0) and (-a ,0), respectively. If a point P moves so that P A^2-P B^2=2k^2, when k is constant, then find the equation to the locus of the point Pdot

If P be any point in the plane of square ABCD, prove that PA^(2)+PC^(2)=PB^(2)+PD^(2)

The point P of the curve y^(2)=2x^(3) such that the tangent at P is perpendicular to the line 4x-3y +2=0 is given by

Find the locus of the point P such that PA^2+PB^2=2c^2 :where A(a,0),B(-a,0) and 0 lt |a| lt |c|.