\( x^{2}+y^{2}=16 \) is the auxilliary circle of (A) \( 9 x^{2}-16 ...

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\( x^{2}+y^{2}=16 \) is the auxilliary circle of
(A) \( 9 x^{2}-16 y^{2}-144=0 \)
(B) \( 16 x^{2}-9 y^{2}+144=0 \)
\( \mathrm{P} \)
(C) \( 9(x-y)^{2}-16(x+y)^{2}-288=0 \)
(D) \( 16(x-y)^{2}-9(x+y)^{2}+288=0 \)
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