The equation of the tangent line to the curve $y = x^2-2x+5$ which is parallel to the line $4x - y + 1 = 0$ is

$4x-y-4=0$

The correct answer is Option (2) → $4x-y-4=0$ **

The line $4x - y + 1 = 0$ has slope:

$y = 4x + 1 \;\Rightarrow\; m = 4$

For the tangent to be parallel, its slope must also be $4$.

Curve: $y = x^2 - 2x + 5$

Derivative:

$y' = 2x - 2$

Set slope equal to $4$:

$2x - 2 = 4$

$2x = 6$

$x = 3$

Corresponding $y$:

$y = 3^2 - 2\cdot3 + 5 = 9 - 6 + 5 = 8$

Equation of tangent at $(3,8)$ with slope $4$:

$y - 8 = 4(x - 3)$

$y = 4x - 12 + 8$

$y = 4x - 4$

Answer: $y = 4x - 4$