Find a point on the curve y = (x – 2)² at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).

We know that if a tangent is parallel to the chord joining the points (2,0) and (4,4), then

Slope of the tangent = slope of the curve………….(1)

And, the slope of the curve =

Now, slope of the tangent to the given curve at a point (x,y) is:

Now, from (1) we have,

2(x -2) = 2

⇒ x-2 = 1

⇒ x =3

So, when x = 3 then y = (3-2)² = 1

Therefore, required points are (3,1).