Mathematics

Mathematics

Problem

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

|PQ|

is equal to (a)

\frac{5\sqrt{3}}{2}

(b)

\frac{5\sqrt{5}}{2}

(c)

\frac{2\sqrt{5}}{3}

(d)

\frac{3\sqrt{5}}{2}

(a)

\frac{5\sqrt{3}}{2}

(b)

\frac{5\sqrt{5}}{2}

(c)

\frac{2\sqrt{5}}{3}

(d)

\frac{3\sqrt{5}}{2}

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