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If the line y=m x+1 is tangent to the p...

If the line `y=m x+1` is tangent to the parabola `y^2=4x ,` then find the value of `m`.

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To solve the problem, we need to find the value of \( m \) such that the line \( y = mx + 1 \) is tangent to the parabola \( y^2 = 4x \). ### Step 1: Substitute the line equation into the parabola equation We start by substituting \( y \) from the line equation into the parabola equation. The parabola is given by: \[ y^2 = 4x \] Substituting \( y = mx + 1 \) into the parabola equation gives: ...
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