The locus of the mid-points of the chords of the circle x² y²=16 which are tangents to the hyperbola 9x²−16y²=144 is :
A. (x² y²)²=16x²−9y²
B. (x² y²)²=9x²−16y²
C. (x²−y²)²=16x²−9y²
D. none of these