Let x and y be real variables satisfying x2+y2+8x−10y−40=0.Let a=max(x+2)2+(y−3)2 and b=min(x+2)2+(y−3)2. Then,

x2+y2+8x−10y−40=0The center of the circle is (4, 5).its radius is 9.Distance of the center (-4,5) from the point (-2,3) is 4+4=22.Therefore,     a=22+9 and b=−22+9∴     a+b=18    a−b=42    a⋅b=81−8=73