Two ends A \& B of a straight line segment of constant length 'c' s...

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Two ends A \& B of a straight line segment of constant length 'c' slide upon the fixed rectangular axes OX \& OY respectively. If the rectangle OAPB is completed. Then find locus of the foot of the \( \mathrm{P} \) perpendicular drawn from \( P \) to \( A B \).
(A) \( x^{2 / 3}+y^{2 / 3}=c^{2 / 3} \)
(B) \( x^{2 / 3}+y^{2 / 3}=c^{1 / 3} \)
(C) \( x^{1 / 3}+y^{1 / 3}=c^{2 / 3} \)
(D) \( x^{1 / 3}+y^{1 / 3}=c^{1 / 3} \)
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