A) \[{{\tan }^{-1}}\left( \frac{4}{3} \right)\]
B) \[{{\tan }^{-1}}(1)\]
C) \[{{90}^{o}}\]
D) \[{{\tan }^{-1}}\left( \frac{3}{4} \right)\]
Correct Answer: D
Solution :
\[y={{x}^{2}}\] Þ \[\frac{dy}{dx}={{m}_{1}}=2x\] Þ \[{{\left( \frac{dy}{dx} \right)}_{(1,\,1)}}=2={{m}_{1}}\] and \[x={{y}^{2}}\] Þ \[1=2y\,\frac{dy}{dx}\] Þ \[\frac{dy}{dx}={{m}_{2}}=\frac{1}{2y}\] Þ \[{{\left( \frac{dy}{dx} \right)}_{(1,\,1)}}=\frac{1}{2}\] \[\therefore \]Angle of intersection, \[\tan \theta =\frac{{{m}_{1}}-{{m}_{2}}}{1+{{m}_{1}}{{m}_{2}}}\]=\[\frac{2-\frac{1}{2}}{1+2\times \frac{1}{2}}\]=\[\frac{3}{4}\] Þ\[\theta ={{\tan }^{-1}}(3/4)\].
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