# 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)

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)