x2+y2−4y=0 ⇒x2+y2−4y+4=4 ⇒x2+(y−2)2=22 The circle passes through origin. Given centre of circle (0,2) and radius is 2. Distance between (0,2 and (4,5) =√(4−0)2+(5−2)2=5 As the circle can touch internally or externally to the given circle. R−2≤5 and R+2≥5 R≤7 and R≥3 ∴3≤R≤7
