JEE Math Practice Question

The locus of the midpoints of the chord of the circle, x2 + y2 = 25 which is tangent to the hyperbola, $${{{x^2}} \over 9} - {{{y^2}} \over {16}} = 1$$ is :

1. A.(x2 + y2)2 $$-$$ 9x2 + 16y2 = 0
2. B.(x2 + y2)2 $$-$$ 9x2 + 144y2 = 0
3. C.(x2 + y2)2 $$-$$ 16x2 + 9y2 = 0
4. D.(x2 + y2)2 $$-$$ 9x2 $$-$$ 16y2 = 0