Equation of a circle with centre (– 4, 3) touching internally and containing the circle x2+y2=1 is

Let the equation of the required circle be.           (x+4)2+(y−3)2=r2                                  (i)If (i) touches the circle x2+y2=1 internally         (ii)the distance between the centres (- 4, 3) and (0, 0) of these circles is equal to the difference of their radii⇒ 42+32=r−1⇒r=5+1⇒r=6So that an equation of the required circle isx2+y2+8x−6y−11=0.