If the point `(x , y)` is equidistant from the points `(a+b , b-a)` and `(a-b , a+b)` , prove that `b x=a ydot`

A point A (2,-1) is equidistant from the points (b,-7) and (- 3, b). Find b.

If P(x, y) is a point equidistant from the points A(6, -1) nad B(2, 3), show that x-y = 3.

Find a point on the y-axis which is equidistant from the points A(6, 5) and B(-4, 3).

Find the co-ordinates of the point, which is equidistant from four points (0, 0, 0), (a, 0, 0), (0, b, 0) and (0, 0, c).

If the equation of the locus of a point equidistant from the points (a_1, b_1) and (a_2, b_2) is (a_1-a_2)x+(b_1-b_2)y+c=0 , then the value of c is a a2-a2 2+b1 2-b2 2 sqrt(a1 2+b1 2-a2 2-b2 2) 1/2(a1 2+a2 2+b1 2+b2 2) 1/2(a2 2+b2 2-a1 2-b1 2)

Find the point which is equidistant from the points (a,0,0),(0,b,0),(0,0,c) and (0,0,0),a,b and c being non-zero reals.

Find a relation between x and y such that the point (x , y) is equidistant from the points (7, 1 ) and (3, 5) .

Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (- 3, 4).

Prove that the points (a ,b+c),(b ,c+a)a n d(c ,a+b) are collinear.

Prove that the product of the lengths of the perpendiculars drawn from the points (sqrt(a^2-b^2), 0) and (-sqrt(a^2-b^2), 0) to the line x/a cos theta+y/b sin theta=1 is b^2 .