The locus of the midpoints of the chord of the circle, \( x^{2}+y^{2}=25 \) which is tangent to the hyperbola, \( \frac{…

\( \left(x^{2}+y^{2}\right)^{2}-9 x^{2}+16 y^{2}=0 \)

\( \left(x^{2}+y^{2}\right)^{2}-9 x^{2}+144 y^{2}=0 \)

\( \left(x^{2}+y^{2}\right)^{2}-16 x^{2}+9 y^{2}=0 \)

\( \left(x^{2}+y^{2}\right)^{2}-9 x^{2}-16 y^{2}=0 \)