Find the equation of the tangent line to the curve y = x² – 2x +7 which is

(a) Parallel to the line 2x – y + 9 = 0

(b) Perpendicular to the line 5y – 15x = 13.

The equation of the given curve is. (-∞,-1)

On differentiating with respect to x, we get:

(3, ∞)

(a) The equation of the line is 2x − y + 9 = 0.

2x − y + 9 = 0 ⇒ y = 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.

Therefore, we have:

2 = 2x – 2

(-∞, –1) 

Now, x = 2

(3, ∞) y = 4 − 4 + 7 = 7

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