The centres of those circles which touch the circle

Question:

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 :-

  1.  A parabola

  2.  A circle

  3.  An ellipse which is not a circle

  4.  A hyperbola

Correct Option: 1

Solution:

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