If the angle between the circles x^2+y^2+2 x-4 y+1=0 and x^2+y^2-4 x-2 y+c=0 is 4 , then c=

Step-by-step solution

aligned & (a) x^2+y^2+2 x-4 y+1=0 & g₁=1, f₁=-2, c₁=1 & x^2+y^2-4 x-2 y+c=0 & g₁=-2, f₂=-1, c₂= c aligned Now, angle between the circles is aligned & ( )= c₁+c₂-2 ( ~g ₁ ~g ₂+ f ₁ f ₂ ) 2 g₁^2+f₁^2-c₁ g₂^2+f₂^2-c₂ & ( 4 )= 1+c-2(1 (-2)+(-2)(-1)) [2] 1+4-1 4+1-c & 1 2 = 1+c 4 5-c 16(5-c)=2(1+c)^2 & c^2+10 c-39=0 (c-3)(c+13)=0 & c=3 or c=-13 aligned