JEE Main & Advanced
Mathematics
Applications of Derivatives
Question Bank
Mock Test - Application of Derivatives
question_answer
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 \[\left| PQ \right|\] 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 \[PQ=\frac{3\sqrt{5}}{2}\]