If the line $y=mx+1$ is a tangent to the parabola $y^2=4x$, then the value of $m$ is:

Solution

1. The condition for the line $y=mx+c$ to be tangent to $y^2=4ax$ is $c=a/m$.
2. Here $a=1$ and $c=1$.
3. Substituting these values, $1 = 1/m$.
4. Solving for $m$ gives $m=1$.
5. Hence the answer is (A).