Find the locus of the mid points of the chords of the circle x2 + y2 = 16, which are tangent to the hyperbola 9x2 – 16y2 = 144. 

1
(x2 + y2)2 = 16x2 – 9y2
2
(x2 + y2)2 = 16x2 + 9y2 
3
(x2 + y2)2 = 9x2 – 16y2
4
(x2 + y2)2 = 9x2 + 16y2
5
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