Calculus

Application of Derivatives

Medium

applied

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)

(2, 3)

(2, -3)

(3, 1)

✅ Correct Option: 4

The chord joins points $(2, 0)$ and $(4, 4)$ .

Using the slope formula:

$\text{Slope of chord} = \frac{4 - 0}{4 - 2}$

$= \frac{4}{2}$

$= 2$

For the tangent to be parallel to the chord, it must have the same slope.

Given: $y = (x - 2)^2$

Taking the derivative:

$\frac{dy}{dx} = 2(x - 2)$

Setting the derivative equal to 2:

$2(x - 2) = 2$

$x - 2 = 1$

$x = 3$

Substituting $x = 3$ into the original equation:

$y = (3 - 2)^2$

$= (1)^2$

$= 1$

Therefore, the point is $(3, 1)$ .

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Solution

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