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(B) The parametric coordinates of a point on the hyperbola $xy = c^{2}$ are $(ct, c/t)$.The equation of the normal at point $t$ is given by $x t^{3} -

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$t^{3}t' = -1$

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(B) The parametric coordinates of a point on the hyperbola $xy = c^{2}$ are $(ct, c/t)$.The equation of the normal at point $t$ is given by $x t^{3} - yt - ct^{4} + c = 0$.If this normal meets the curve again at point $t'$,then the coordinates $(ct', c/t')$ must satisfy the normal equation.Substituting $(ct', c/t')$ into the equation: $(ct')t^{3} - (c/t')t - ct^{4} + c = 0$.Dividing by $c$ (assuming $c 
eq 0$): $t't^{3} - t/t' - t^{4} + 1 = 0$.Multiplying by $t'$: $t'^{2}t^{3} - t - t't^{4} + t' = 0$.Rearranging terms: $t^{3}t'(t' - t) + (t' - t) = 0$.$(t' - t)(t^{3}t' + 1) = 0$.Since $t 
eq t'$,we must have $t^{3}t' + 1 = 0$,which implies $t^{3}t' = -1$.

The normal to the rectangular hyperbola $xy = c^{2}$ at the point $t$ meets the curve again at a point $t'$,such that

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