question_answer

If the area (in sq. units) bounded by the parabola \[{{y}^{2}}=4\lambda x\] and the line \[y=\lambda x,\lambda >0,\]is \[\frac{1}{9},\] then \[\lambda \] is equal to : [JEE Main 12-4-2019 Afternoon]

A) 24       

B) 48

C) \[4\sqrt{3}\]                

D) \[2\sqrt{6}\]

Correct Answer: A

Solution :

Area \[=\frac{1}{9}=\int\limits_{0}^{\frac{4}{\lambda }}{\left( \sqrt{4\lambda x}-\lambda x \right)}dx\]\[\Rightarrow \lambda =24\]