The circles `x^2 + y^2 + 2ax-c^2 = 0` and `x^2 + y^2 + 2bx-c^2=0` intersect at A and B. A line through A meets one circle at P and a parallel line through B meets the other circle at Q. Show that the locus of the mid-point of PQ is a circle.

Two equal circles intersect in P and Q.A straight line through P meets the circles in A and B. Prove that QA=QB

x^(2)+y^(2)=16 and x^(2)+y^(2)=36 are two circles.If P and Q move respectively on these circles such that PQ=4 then the locus of mid-point of PQ is a circle of radius

If a tangent to the circle x^(2)+y^(2)=1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is :

If a tangent to the circle x^(2)+y^(2)=1 intersects the coordinate axes at distinct point P and Q. then the locus of the mid- point of PQ is

If a line through P(-2,3) meets the circle x^(2)+y^(2)-4x+2y+k=0 at A and B such that PA.PB =31 then the radius of the circle is

Consider the circle x^2 + y^2 + 4x+6y + 4=0 and x^2 + y^2 + 4x + 6y + 9=0, let P be a fixed point on the smaller circle and B a variable point on the larger circle, the line BP meets the larger circle again at C. The perpendicular line 'l' to BP at P meets the smaller circle again at A, then the values of BC^2+AC^2+AB^2 is