Let `S_1:,x^2+y^2-2px -4y+1 =0`and `S_2: x^2+y^2 +4x-2qy-1=0 ` be two circles, `p. q epsilon R` If `S_2 =0` bisects the circumference of the circle `S_1=0` such that radius of the circle `S_2=0` is least then

Show that the circle x^2+y^2+4x+4y-1=0 bisects the circumference of the circle x^2+y^2+2x-3=0 .

Show that the circle x^2+y^2+4x+4y-1=0 bisects the circumference of the circle x^2+y^2+2x-3=0 .

A circle x^2 +y^2 + 4x-2sqrt2 y + c = 0 is the director circle of circle S_1 and S_1 is the director circle of circle S_2 , and so on. If the sum of radii of all these circles is 2, then find the value of c.

The circumference of the circle x^2+y^2-2x+8y-q=0 is bisected by the circle x^2+ y^2+4x+12y+p=0 , then p+q is equal to

The circle S=0 cuts the circle x^(2)+y^(2) -4x+2y-7=0 orthogonally if (2,3) is the centre of the circle S=0 then its radius is

If S_1=x^2+y^2+2g_1x+2f_1y+c_1=0 and S_2=x^2+y^2+2g_2x +2f_2y+c_2=0 are two circles with radii r_1 and r_2 respectively, show that the points at which the circles subtend equal angles lie on the circle S_1/r_1^2=S_2/r_2^2

Statement 1 : Let S_1: x^2+y^2-10 x-12 y-39=0, S_2 x^2+y^2-2x-4y+1=0 and S_3:2x^2+2y^2-20 x-24 y-78=0. The radical center of these circles taken pairwise is (-2,-3)dot Statement 2 : The point of intersection of three radical axes of three circles taken in pairs is known as the radical center.

Statement 1 : Let S_1: x^2+y^2-10 x-12 y-39=0, S_2 x^2+y^2-2x-4y+1=0 and S_3:2x^2+2y^2-20 x-24 y-78=0. The radical center of these circles taken pairwise is (-2,-3)dot Statement 2 : The point of intersection of three radical axes of three circles taken in pairs is known as the radical center.

A circle x^2 +y^2 + 4x-2sqrt2 y + c = 0 is the director circle of circle S_1 and S_2 , is the director circle of circle S_1 , and so on. If the sum of radii of all these circles is 2, then find the value of c.

The circumference of the circle x^(2)+y^(2)-2x+8y-q=0 is bisected by the circle x^(2)+y^(2)+4x+12y+p=0, then p+q is equal to