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\( A B \) is a variable line sliding between the co-ordinate axes in such a way that \( A \) lies on \( \mathrm{X} \)-axis and \( \mathrm{B} \) lies on \( \mathrm{Y} \)-axis. If \( \mathrm{P} \) is a variable point on \( \mathrm{AB} \) such that \( \mathrm{PA}=b, \mathrm{~PB}=a \) and \( \mathrm{AB}=a+b \), then equation of locus
\( \mathrm{P} \) of \( P \) is
(A) \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \)
(B) \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \)
(C) \( x^{2}+y^{2}=a^{2}+b^{2} \)
(D) \( x^{2}-y^{2}=a^{2}+b^{2} \)
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