A curve is given by the equations x=sec2θ,   y=cotθ. If the tangent at P where θ=π4 meets the curve again at Q, then [PQ] is, where [ . ] represents the greatest integer function _____

dydx=-12cot3θ=12  at  θ=π4Also, the point P for θ=π4  is  2,1Equation of tangent is y-1=-12x-2   or  x+2y-4=0       (1)This meets the curve whose Cartesian equation on eliminating θ  by  sec2θ-tan2θ=1 isy2=1x-1                                                (2)Solving (1) and (2) we get y=1,-12∴   x=2,5Hence, P is (2, 1) as given and Q is 5,-12. Therefore,PQ=454=352