The centre of the circle which intersects the circle x^2+y^2-2 x-2 y-2=0 orthogonally and passes through the point (2,0) and touches the X -axis is

Step-by-step solution

Let equation of circle, Whose centre is =(-g,-f) Circle passes through the point (2,0) , so this point satisfy the circle. 4+0+4 g+0+c=0 From Eqs. (ii) and (iii), we get array rlrl 4+4 g+g^2 & =0 (g+2)^2=0 g & =-2 & & c & =4 array Now, circle Eq. (i) intersect the circle x^2+y^2-2 x-2 y-2=0 orthogonally So, condition of orthogonality aligned 2 g₁ g₂+2 f₁ f₂ & =c₁+c₂ 2(-2)(-1)+2 f (-1) & =4-2 4-2 f & =2 4-2 & =2 f f & =1 aligned Hence, coordinate of centre is (2,-1) .