Find the equation of the tangent line to the curve `y=x^2-2x+7`which is(a) parallel to the line `2x y + 9 = 0`(b) perpendicular to the line `5y - 15 x = 13`.

Explanation

(a)

The equation of the given curve is `y=x^2-2x+7`

On differentiating with respect to `x`, we get:

`dy/dx=2x-2`

The equation of the line is `2x-y+9=0impliesy=2x+9`

This is of the form `y=mx+c`

Slope of the line =`2`

If a tangent is parallel to the line `2x−y+9=0`, then the slope of the tangent is equal to the slope of the line.
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