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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).
Asked by Manish Last Modified
Answer 
Slope of tangent at a point (x,y) on the given curve is
It is told that the tangent is parallel to the chord joining (2,0) and (4,4). So slopes of the two lines i.e the tangent and the chord should be equal.
Slope of chord is
So 2(x-2) = 2
So x=3
The corresponding y coordinate can be found by putting x=3 on the equation of the curve. So y=.
Answer = (3,1)
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Harshit Bhardwaj
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).
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