A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{4}\]
D) \[\frac{\pi }{6}\]
Correct Answer: B
Solution :
Any tangent to \[{{y}^{2}}=4x\] is \[y=mx+\frac{1}{m}\] Since it passes throguh (1, 4), we have \[4=m+\frac{1}{m}\] \[\Rightarrow \]\[{{m}^{2}}-4m+1=0\]\[\Rightarrow \]\[{{m}_{1}}+{{m}_{2}}=4\], \[{{m}_{1}}{{m}_{2}}=1\] \[\Rightarrow \]\[|{{m}_{1}}-{{m}_{2}}|=2\sqrt{3}\] If \[\theta \] is the required angle, then \[\tan \theta =\frac{2\sqrt{3}}{1+1}=\sqrt{3}\] \[\Rightarrow \] \[\theta =\frac{\pi }{3}\].
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