JEE Main & Advanced
JEE Main Paper (Held On 10 April 2015)
question_answer
Let the tangents drawn to the circle, \[{{x}^{2}}+{{y}^{2}}=16\]from the point P(0/ h) meet me r-axis at points A and B. If the area of \[\Delta APB\]is minimum, men h is equal to :
JEE Main Online Paper (Held On 10 April 2015)
A)\[4\sqrt{2}\]
B)\[4\sqrt{3}\]
C)\[3\sqrt{2}\]
D)\[3\sqrt{3}\]
Correct Answer:
A
Solution :
\[OP=\frac{4}{\sin \theta }\] \[OB=\frac{4}{\cos \theta }\] Area\[=OP\times OB=\frac{16}{\sin \theta \cos \theta }=\frac{32}{\sin 2\theta }\] Least value \[\sin 2\theta =1\theta ={{45}^{o}}\]