Consider the circle `x^2+y^2-10x-6y+30=0`. Let O be the centre of the circle and tangent at A(7,3) and B(5, 1) meet at C. Let S=0 represents family of circles passing through A and B, then

The circle x^2 + y^2 - 4x + 6y + c = 0 touches x axis if

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 circle x^2 + y^2 + 8x + 10y - 8 = 0 (i) Find its radius of the circle x^2 + y^2 + 8x + 10y - 8 = 0 (ii) Find the equation of the circle with centre at C and passing through (1,2).

Consider the family of circles x^(2)+y^(2)-2x-6y-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 . If the circle x^(2)+y^(2)-10x+2y+c=0 is orthogonal to S=0 , then the value of c is

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

The center(s) of the circle(s) passing through the points (0, 0) and (1, 0) and touching the circle x^2+y^2=9 is (are)

If one of the diameters of the circle x^2+y^2-2 x-6 y+6 =0 is a chord to the circle with centre at (2,1) then the radius of the circle is equal to.

Find the equation of the circle passing through the points (2,3) and (-1,-1) and whose centre is on the line x-3y-11=0.

If the line a x+b y=2 is a normal to the circle x^2+y^2-4x-4y=0 and a tangent to the circle x^2+y^2=1 , then a and b are