Question

The line \(y = mx + 1\) is a tangent to the curve \(y^2 = 4x\) if the value of \(m\) is

• A. 1
• B. 2
• C. 3
• D. \(\frac{1}{2}\)

Answer 1

The Correct Option is A

The correct answer is A:1
The equation of the tangent to the given curve is \(y = mx + 1\). Now, substituting \(y = mx + 1\) in \(y^2 = 4x\), we get:
\((mx+1)^2=4x\)
\(m^2x^2+1+2mx-4x=0\)
\(m^2x^2+x(2m-4)+1=0 ...(i)\)
Since a tangent touches the curve at one point, the roots of equation (i) must be equal. Therefore, we have:
Discriminant=0
\((2m-4)^2-4(m^2)(1)=0\)
\(=4m^2+16-16m-4m^2=0\)
\(16-16m=0\)
\(m=1\)
Hence, the required value of m is 1.
The correct answer is A