For which value of m is the line y = mx + 1 a tangent to the curve `y^2=4x`

Options

A. 1/2
B. 1
C. 2
D. 3

Answer

Option 2

Explanation

If we put `y=m x+1` in `y^{2}=4 x` then we get
$$ \begin{aligned} &(\mathrm{mx}+1)^{2}=4 \mathrm{x} \\ &\Rightarrow \mathrm{m}^{2} \mathrm{x}^{2}+1+2 \mathrm{mx}-4 \mathrm{x}=0 \end{aligned} $$
Tangent touches a curve at one point so descriminant of the equation should be zero. (the quadratic equation has only one solution or two real and equal solutions)
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