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)

Solution:

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line.

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.

Hence,

the slope of chord is (4 - 0)/(4 - 2)

= 4/2

= 2

Now, the slope of the tangent to the given curve is,

dy/dx

= 2(x - 2)

Since the slope of the tangent

= the slope of the chord.

Hence,

2(x - 2) = 2

⇒ x - 2 = 1

⇒ x = 3

When, x = 3

Then,

y = (3 - 2)²

= 1

Hence, the point on the curve is (3, 1)

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.3 Question 8

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)

Summary:

The 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) is (3, 1)