A) \[m=1\]
B) \[~m=2\]
C) \[m=4\]
D) \[~m=3\]
Correct Answer: A
Solution :
Key Idea: The line \[y=mx+1\]touches the parabola\[{{y}^{2}}=4ax,\] if \[c=\frac{a}{m}.\] Given that, equation of line is \[y=mx+1\] ?(i) and equation of parabola is \[{{y}^{2}}=4x\] ?(ii) If the line \[y=mx+1\]touches the parabola\[{{y}^{2}}=4x\] then it will intersect \[{{(mx+1)}^{2}}=4x\] or \[{{m}^{2}}{{x}^{2}}+2x(m-2)+1=0\] only one point. i.e., Discriminant, \[{{b}^{2}}=4ac\] \[\Rightarrow \] \[4{{(m-2)}^{2}}=4{{m}^{2}}\] \[\Rightarrow \] \[4-4m=0\] \[\Rightarrow \] \[m=1\]
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