question_answer

The area of the region bounded by the curves  \[{{x}^{2}}+{{y}^{2}}=9\] and x + y = 3 is

A) \[\frac{9\pi }{4}+\frac{1}{2}\]                    

B)  \[\frac{9\pi }{4}-\frac{1}{2}\]

C) \[9\left( \frac{\pi }{4}-\frac{1}{2} \right)\]            

D) \[9\left( \frac{\pi }{4}+\frac{1}{2} \right)\]

Correct Answer: C

Solution :

Area of required region     \[x\pm y=0\] Area of circle ? Area of \[\sqrt{2}\]      \[=2\times \left( 8 \right)=16\]      \[{{x}^{2}}-{{y}^{2}}={{8}^{2}}\]