Locus of the midpoints of chords of one conic that touch another conic

1. A.
   $\left( x^{2} + y^{2} \right)^{2} - 16x^{2} + 9y^{2} = 0$
2. B.
   $\left( x^{2} + y^{2} \right)^{2} - 9x^{2} + 144y^{2} = 0$
3. C.
   $\left( x^{2} + y^{2} \right)^{2} - 9x^{2} - 16y^{2} = 0$
4. D.
   $\left( x^{2} + y^{2} \right)^{2} - 9x^{2} + 16y^{2} = 0$

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1. A.
   $y^{3}(x - 2) = x^{2}$
2. B.
   $x^{3}(x - 2) = y^{2}$
3. C.
   $y^{2}(x - 2) = x^{3}$
4. D.
   $x^{2}(x - 2) = y^{3}$

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