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`.

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.

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).

Consider the family of circles x^(2)+y^(2)-2x-2ay-8=0 passing through two fixed points A and B . Also, S=0 is a cricle of this family, the tangent to which at A and B intersect on the line x+2y+5=0 . The distance between the points A and B , is

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 equation of the circle which passes through the points (3, -2), (-2, 0) and has its centre on the line 2x - y =3.

Find the equation of the two tangents from the point (0, 1 ) to the circle x^2 + y^2-2x + 4y = 0

If the lines x+y=6 and x+2y=4 are diameters of the circle which passes through the point (2, 6), then find its equation.

Find the equations of the tangents to the circle x^(2) + y^(2) -8y - 8 = 0 which are parallel to the line 5 x -2 y = 2.

Find the equation of the circle passing through (1,2) and which is concentric with the circle x^2+y^2+11x-5y+3=0.