Find a point on the parabola `y=(x-4)^2` , where the tangent is parallel to the chord joining (4, 0) and (5, 1).

Answer

The point is `(9 / 2,1 / 4)`

Explanation

As the tangent is parallel to the chord joining `(4,0)` and `(5`, 1),
we would get,

$$ \begin{aligned} &2(x-4)=(1-0) /(5-4)=1 \\ &(x-4)=1 / 2 \\ &x=4 + 1 / 2 = 9 / 2 \end{aligned} $$
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