JEE Main & Advanced
JEE Main Paper (Held on 12-4-2019 Afternoon)
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 \[=\frac{1}{9}=\int\limits_{0}^{\frac{4}{\lambda }}{\left( \sqrt{4\lambda x}-\lambda x \right)}dx\]\[\Rightarrow \lambda =24\]