A straight line passes through the point (2, 0) and has gradient m. Find the two values of m for which the line is a tangent to the curve y = x^2 − 4x + 5. For each value of m, find the coordinates of the point where the line touches the curve.

Expert Answers

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`y= x^2-4x+5`

The gradient(n) of the tangent  for the curve is given by;

`dy/dx = 2x-4`

`n=2x-4`

The equation of line passing (2,0) is given by;

`y = mx+c`

Since the line passes through (2,0)

`0 = 2xm+c`

`c = -2m`

The equation of the line is;

`y = mx-2m`

If the...

(The entire section contains 153 words.)

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