A curve is represented by the equation. \( x=\sec ^{2} \) P \( t \)...

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A curve is represented by the equation. \( x=\sec ^{2} \)
P \( t \) and \( y=\cot t \) where \( t \) is the parameter, tangent at

W the point \( P \) on the curve where \( t=\frac{\pi}{4} \) meets the curve again at the point \( Q \) then, \( |P Q| \) is equal to:
(1) \( \frac{5 \sqrt{3}}{2} \)
(2) \( \frac{5 \sqrt{5}}{2} \)
(3) \( \frac{2 \sqrt{5}}{3} \)
(4) \( \frac{3 \sqrt{5}}{2} \)
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