Question

Mark the correct alternative of the following.
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. $1/2$

Answer 1

The correct option is A $1$

Given equation of the tangent to the given curve

$y=mx+1$

Now substituting the value of y in

$y^2=4x$, we get

$\Rightarrow (mx+1{)}^2=4x$

$\Rightarrow m^2{x}^2+1+2mx-4x=0$

$\Rightarrow m^2{x}^2+x(2m-4)+1=0$ ..........$\left(1\right)$

Since, a tangent touches the curve at one point, the root of equation $\left(1\right)$ must be equal.

Thus, we get

Discriminant, $D=b^2-4ac=0$

$(2m-4{)}^2-4(m^2\left)\right(1)=0$

$\Rightarrow 4m^2-16m+16-4m^2=0$

$\Rightarrow -16m+16=0$

$\Rightarrow m=1$.