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Question -

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



Answer -

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 givencurve at a point (xy) is given by,

Since the slope of the tangent = slope of the chord, wehave:

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

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