# The line y = mx +

It is given that the equation of the tangent to the given curve is

y = mx + 1

Now, substituting the value of y in y2 = 4x, we get

(mx + 1)2 = 4x

m2x2 + 1 + 2mx - 4x =0

m2x2 + x(2m - 4) + 1 = 0………………..(1)

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

Thus, we get

Discriminant = 0

(2m - 4)2 – 4(m2)(1) = 0

4m2 + 16 - 16m - 4m2 =0

16 – 16m = 0

m =1

Therefore, the required value of m is 1.

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