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)`

Derive the equation of the line passing through two points ( x_ 1,y_1) and ( x_2,y_2)

Property 1: The equation of the family of circles passing through the point of intersection of two given circles.

.The equation of the circle passing through three non-collinear points P( x_1,y_1 ) Q( x_2,y_2 ) and R( x_3,y_3 ) is

. The equation of the circle passing through three non-collinear points P(x_(1),y_(1))Q(x_(2),y_(2)) and R(x_(3),y_(3)) is

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.

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2