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# Find a unit vector that is parallel to the line tangent to the parabola y = x^{2} at the point (2, 4).

**Solution:**

Given parabola y = x^{2}

Point (2, 4)

The slope of the tangent line to the parabola at (2,4) can be written as

(dy/dx) at (2,4) = 2x at (2,4) =4

So, any line parallel to the tangent line has slope ‘4’

Let us assume the unit vector is ±(i + 4j)

The length of the vector is √(1^{2} + 4^{2}) = √17

So, the required unit vectors are ±(i + 4j)/√17

## Find a unit vector that is parallel to the line tangent to the parabola y = x^{2} at the point (2, 4).

**Summary:**

The unit vector that is parallel to the line tangent to the parabola y = x^{2} at the point (2, 4) is ±(i + 4j)/√17.

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