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.

C : x^(2) + y^(2) - 2x -2ay - 8 = 0 , a is a variable C represents a family of circles through two fixed points whose co-ordinates are

Show that equation x^(2)+y^(2)-2ay-8=0 represents,for different values of 'a,asystem of circles passing through two fixed points A, B on the X-axis,and find the equation ofthat circle of the system the tangents to which at AB meet on the line x+2y+5=0 .

Statement 1 : The equation x^2+y^2-2x-2a y-8=0 represents, for different values of a , a system of circles passing through two fixed points lying on the x-axis. Statement 2 : S=0 is a circle and L=0 is a straight line. Then S+lambdaL=0 represents the family of circles passing through the points of intersection of the circle and the straight line (where lambda is an arbitrary parameter).

Show that the equation (3-2k) x-(2+k)y=5-k, where k is real represents a family of lines all passing through a fixed point. Find the co-ordinates of this fixed point.

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

The value of k ,such that the equation, 2x^(2)+2y^(2)-6x+8y+k=0 represents a point circle,is

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))