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
Answer & explanation
Correct answer: option 2
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: $y = 4x - 4$