Two tangents from one point

8 written marks

A line through \(P=(0,1)\) has equation \(y=mx+1\). The curve is \(y=x^2-2x+5\). Do not use differentiation.

1. Form a quadratic equation for the x-coordinates of intersections.

   [2]

2. Find the two values of \(m\) for which the line is tangent to the curve.

   [3]

3. Find the point of contact for each tangent.

   [3]

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