Consider two circles `S, =x^2+y^2 +8x=0 and S_2=x^2+y^2-2x=0`. Let `DeltaPOR` be formed by the common tangents to circles `S_1 and S_2`, Then which of the following hold(s) good?

Consider the circles S_(1):x^(2)+y^(2)=4 and S_(2):x^(2)+y^(2)-2x-4y+4=0 which of the following statements are correct?

Consider two circles S_1=x^2+(y-1)^2=9 and S_2=(x-3)^2+(y-1)^2=9 , now for these circles match the following :

For the circles S_1: x^2 + y^2-4x-6y-12 = 0 and S_2 : x^2 + y^2 + 6x + 4y-12=0 and the line L.:x+y=0 (A) L is common tangent of S_1 and S_2 (B) L is common chord of S_1 and S_2 (C) L is radical axis of S_1 and S_2 (D) L is perpendicular to the line joining the cente of S_1 & S_2

If the circles given by S-=x^2+y^2-14x+6y+33=0 and S' -=x^2+y^2-a^2=0(ainN) have 4 common tangents, then the possible number of circles S' =0 is

If the circles given by S-=x^(2)+y^(2)-14x+6y+33=0 and S'-=x^(2)+y^(2)-a^(2)=0(a in N) have 4 common tangents, then the possible number of circles S'=0 is

If S-=x^2+y^2-4x=0, S'-=x^2+y^2+8x=0 and AB is a direct common tangent to the two circles where A,B are points of contact then find the angle subtended by AB at origin.

Consider the circles C_(1):x^(2)+y^(2)-4x+6y+8=0;C_(2):x^(2)+y^(2)-10x-6y+14=0 Which of the following statement(s) hold good in respect of C_(1) and C_(2)?