A) \[{{\tan }^{-1}}(3)\]
B) \[{{\tan }^{-1}}(2)\]
C) \[\frac{\pi }{2}\]
D) \[\frac{\pi }{4}\]
Correct Answer: A
Solution :
For curve \[{{y}^{2}}=4x\] Þ \[\frac{dy}{dx}=\frac{4}{2y}\] \\[{{\left( \frac{dy}{dx} \right)}_{(1,\,2)}}=1\] and for curve \[{{x}^{2}}+{{y}^{2}}=5\] Þ \[\frac{dy}{dx}=\frac{-x}{y}\] \ \[{{\left( \frac{dy}{dx} \right)}_{(1,\,2)}}=\frac{-1}{2}\] \ Angle between the curves is \[\theta ={{\tan }^{-1}}\left| \,\frac{\frac{-1}{2}\,-1}{1+\left( \frac{-1}{2} \right)}\, \right|={{\tan }^{-1}}(3)\].
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