Prove that the following pairs are orthogonal. (i) \( 16 x^{2}+y^{2}=c \) and \( y^{16}=k x \) (...

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Prove that the following pairs are orthogonal.
(i) \( 16 x^{2}+y^{2}=c \) and \( y^{16}=k x \)
(ii) \( y=x+c e^{-x} \) and \( x+2=y+k e^{-y} \)
(iii) \( x^{2}-y^{2}=c \) and \( x y=k \)
where \( c \) and \( k \) arbitrary constant.
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