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Question

The equation of the tangent to the parabola y = x2 - 2x + 3 at the point (2,3) is .

A
x = 4y - 1
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B
x = 2y - 1
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C
y = 4x - 1
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D
y = 2x - 1
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Solution

The correct option is D y = 2x - 1
Given equation of parabola is y=x22x+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.

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