Given that the line y = mx + 1 is the tangent to the parabola y2 = 4x. We need to find the value of m.
Let us substitute the value in the equation of parabola.
⇒ (mx + 1)2 = 4x
⇒ m2x2 + 2mx + 1 = 4x
⇒ m2x2 + (2m - 4)x + 1 = 0
The quadratic will have similar roots if the line is tangent to the parabola.
We know that for a quadratic equation ax2 + bx + c = 0 to have equal roots, the condition to be satisfied is b2 - 4ac = 0
⇒ (2m - 4)2 - 4(m2)(1) = 0
⇒ 4m2 - 16m + 16 - 4m2 = 0
⇒ 16 - 16m = 0
⇒ 16m = 16
⇒ m = 1
∴The value of m is 1.
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