A curve is represented by the equations, \( x=\sec ^{2} t \) and \( y= \) \( \cot t \) where \( ...

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A curve is represented by the equations, \( x=\sec ^{2} t \) and \( y= \) \( \cot t \) where \( t \) is a parameter. If the tangent at the point \( P \) on the curve where \( t=\pi / 4 \) meets the curve again at the point \( Q \) then \( |\mathrm{PQ}| \) is equal to :
(a) \( \frac{5 \sqrt{3}}{2} \)
(d) \( \frac{5 \sqrt{5}}{2} \)
(c) \( \frac{2 \sqrt{5}}{3} \)
(d) \( \frac{3 \sqrt{5}}{2} \)
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