question_answer

A curve is represented by the equation \[x=se{{c}^{2}}t\]and\[y=cot\text{ }t\], 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 \[\left| PQ \right|\] is equal to

A) \[\frac{5\sqrt{3}}{2}\]

B) \[\frac{5\sqrt{5}}{2}\]

C) \[\frac{2\sqrt{5}}{3}\]

D) \[\frac{3\sqrt{5}}{2}\]

Correct Answer: D

Solution :

[d] Eliminating t gives \[{{y}^{2}}(x-1)=1\]. Equation of the tangent at \[P(2,1)\] is \[x+2y=4\]. Solving with curve \[x=5\] and \[y=-1/2\], we get \[Q\equiv (5,-1/2)\] or \[PQ=\frac{3\sqrt{5}}{2}\]