A fixed circle is cut by circles passing through two given points `A(x_1, y_1) and B(x_2, y_2)`. Show that the chord of intersection of the fixed circle with any one of the circles, passes through a fixed point.

Property 4: The equation of the family of circles passing through two given points P(x_(1),y_(1)) and Q(x_(2),y_(2))

consider a family of circles passing through two fixed points S(3,7) and B(6,5) . If the common chords of the circle x^(2)+y^(2)-4x-6y-3=0 and the members of the family of circles pass through a fixed point (a,b), then

If a circle passing through the point (-1,0) touches y-axis at (0,2) then the length of the chord of the circlealong the x-axis is

Equation of the smaller circle that touches the circle x^(2)+y^(2)=1 and passes through the point (4,3) is