CUET · MATHS · PYQ PAPER 2025
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 :
- A \((3,-1)\)
- B \((2,3)\)
- C \((2,-3)\)
- D \((3,1)\)
Answer & Solution
Correct Answer
(D) \((3,1)\)
Step-by-step Solution
Detailed explanation
Slope of chord: \( m = \frac{4-0}{4-2} = 2 \) Derivative: \( \frac{dy}{dx} = 2(x-2) \) Equate slopes: \( 2(x-2) = 2 \) Solve for \(x\): \( x-2 = 1 \implies x = 3 \) Find \(y\): \( y = (3-2)^2 = 1 \) Point: \( (3,1) \)
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