The centres of those circles which touch the circle, x 2 + y 2 - 8 x - 8 y - 4 = 0 , externally and also touch the x - axis, lie on

Step-by-step solution

Given circle x 2 + y 2 - 8 x - 8 y - 4 = 0 has centre 4 ,   4 and radius 6 . Let h ,   k be the centre of the circle which is touching the given circle externally Then h - 4 2 + k - 4 2 = 6 + k ⇒ h 2 - 8 h + 16 + k 2 - 8 k + 16 = 36 + 12 k + k 2 ⇒ h 2 - 8 h - 20 k - 4 = 0 , Replacing h by x and k   by y , locus is x 2 - 8 x - 20 y - 4 = 0 Which is equation of parabola.