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)`

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

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.

Show that the equation of the chord of the parabola y^2 = 4ax through the points (x_1, y_1) and (x_2, y_2) on it is : (y-y_1) (y-y_2) = y^2 - 4ax

The order of differential equation of family of circles passing through intersection of 3x+4y-7=0 and S=-x^(2)+y^(2)-2x+1=0 is

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

Prove that the equation of a line which passes through the given point (x_(1),y_(1)) and is such that the given point bisects the part intercepted between the axis,is (x)/(x_(1))+(y)/(y_(1))=2

Prove that the equation x^(2)+y^(2)-2x-2ay-8=0, a in R represents the family of circles passing through two fixed points on x-axis.

Find the locus of the middle points of the chords of the circle x^2+y^2=a^2 which pass through a given point (x_1,y_1)