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Which one of the following is the common tangent to the ellipses, \( \frac{x^{2}}{a^{2}+b^{2}}+\frac{y^{2}}{b^{2}}=1 \) and \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{a^{2}+b^{2}}=1 \) ?
\( \mathrm{P} \)
(a) \( a y=b x+\sqrt{a^{4}-a^{2} b^{2}+b^{4}} \)
(b) \( b y=a x-\sqrt{a^{4}+a^{2} b^{2}+b^{4}} \)
(c) \( a y=b x-\sqrt{a^{4}+a^{2} b^{2}+b^{4}} \)
(d) \( b y=a x+\sqrt{a^{4}-a^{2} b^{2}+b^{4}} \)
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