Question

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

Answer 1

The correct option is D $\frac{3\sqrt{5}}{2}$

Hence option (D) is the correct answer