A) \[\frac{1}{7}(1\pm 5\sqrt{3})\]
B) \[\frac{1}{7}(1\pm 5\sqrt{5})\]
C) \[\frac{1}{7}(1\pm 5\sqrt{2})\]
D) \[\frac{1}{7}(1\pm 2\sqrt{5})\]
E) \[\frac{1}{7}(1\pm 3\sqrt{2})\]
Correct Answer: C
Solution :
As \[m\in \left( \frac{1}{2},3 \right)\] \[\therefore \]Line\[y=mx+4\]lies between \[y=3x+1\]and\[2y=x+3\] Slopes of given lines are\[{{m}_{2}}=3,m=m\]and\[{{m}_{1}}=\frac{1}{2}\] \[\therefore \] \[\tan \theta =\frac{3-m}{1+3m}\] and \[\tan \theta =\frac{m-\frac{1}{2}}{1+\frac{m}{2}}\] \[\Rightarrow \] \[\frac{3-m}{1+3m}=\frac{2m-1}{2+m}\] \[\Rightarrow \] \[7{{m}^{2}}-2m-7=0\] \[\therefore \,\,\,m=\frac{2\pm \,\sqrt{4+196}}{2\times 7}\,=\frac{1}{7}\,(1\pm \,5\sqrt{2})\]
You need to login to perform this action.
You will be redirected in
3 sec
