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 \[\sin 2\theta =1\theta ={{45}^{o}}\]