A point on y=(x−3)2 , where the tangent is parallel to the chord joining (3, 0) and (4, 1) is:

Let the point be(x1,y1) . Therefore, y1=(x1−3)2 Now, slope at the tangent at (x1,y1) is 2(x1−3) but it is equal to1.Therefore 2(x1−3)=1 ⇒x1=72 ∴y1=(72−3)2=14 Hence, the point is (72,14)