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The point on the curve $y^{2} = x$ where tangent makes an angle of $45 °$ with the X-axis is

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(12,14)

(14,12)

(4,2)

(2,−2)

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detailed solution

Correct option is B

Let(α,β) be the required pointβ2=α and(dydx)(α,β)=tan45° (∵ y2=x, ∴2ydydx=1) ⇒12β=1⇒β=12 Also, α=β2=(12)2=14 Hence, the required point is(14,12) .

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The point on the curvey2=x where tangent makes an angle of45° with the X-axis is

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The point on the curve $y^{2} = x$ where tangent makes an angle of $45 °$ with the X-axis is