Question

Find the equation of the tangent line to the curve y = x² − 2x + 7 which is parallel to the line 2x − y + 9 = 0 ?

Answer 1

The equation of 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 = 0

`rArry=2x+9`

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

`therefore "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.

Therefore, We have

2 = 2x - 2

2x = 4

x = 2

Now, x = 2

`y=x^2-2x+7`

`rArry=4-4+7`

Thus, the equation of the tangent passing through (2, 7) is given by,

`y-y_1=m(x-x_1)`

y - 7 = 2(x - 2)

`rArry-2x-3 = 0`

Hence, the equation of the tangent line to the given curve (which is parallel to line 2x - y + 9 = 0) is y - 2x - 3 = 0.