Question

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).

Answer 1

If a tangent is parallel to the chord joining the points (2, 0) and (4, 4), then the slope of the tangent = the slope of the chord. 

The slope of the chord is 

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

Since the slope of the tangent = slope of the chord, we have:

Hence, the required point is (3, 1).