Question

The equation of the tangent to the parabola y = $x^2$ - 2x + 3 at the point (2,3) is .

• A. x = 4y - 1
• B. x = 2y - 1
• C. y = 4x - 1
• D. y = 2x - 1

Answer 1

The correct option is D y = 2x - 1

Given equation of parabola is $y=x^2-2x+3$.
Differentiating this w.r.t. x, we get
y' = 2x - 2.
The slope of the tangent to the parabola at (2, 3) is 2(2) - 2 = 2.
The equation of the line passing through (2, 3) and having slope 2 is y = 2x - 1.