The locus of the centre of a circle which cuts orthogonally the circle x2+y2−20x+4=0 and which touchesx=2 is

Let the circle be x2+y2+2gx+2fy+c=0It cuts the circle x2+y2−20x+4=0 orthogonally∴    2(−10g+0×f)=c+4⇒     −20g=c+4Circle (i) touches the line x = 2 i.e. x + Oy - 2 = 0∴ −g+0−212+02=g2+f2−c⇒ (g+2)2=g2+f2−c⇒4g+4=f2−cEliminating c from (ii) and (iii), we get−16g+4=f2+4⇒f2+16g=0Hence, the locus of (−g,−f) is y2−16x=0