Question 5 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at Dec. 4, 2021 by Teachoo

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The point on the curve y
^{
2
}
= x, where the tangent makes an angle of Ο/4 with x-axis is

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Question 5
The point on the curve y2 = x, where the tangent makes an angle of π/4 with x-axis is
(A) (1/2, 1/4) (B) (1/4, 1/2)
(C) (4, 2) (D) (1, 1)
π¦^2=π₯
Slope of the tangent is π π/π π
Finding π π/π π
2y ππ¦/ππ₯=1
π π/π π=π/ππ
Since, the tangent makes an angle of π/4 with x-axis
i.e., π½=π /π
β΄ Slope of tangent =πππ π½
=tanβ‘γπ/4γ
=π
Equating (1) and (2)
π/ππ=π
1=2π¦
2π¦=1
π=π/π
Since, we have to find point on the curve where the tangent makes an angle of π/4 with x-axis
Finding π by putting π=π/π in equation of curve
π^π=π
(π/π)^2=π₯
1/4 =π₯
π=π/π
β΄ Required point = (x, y) = (π/π,π/π).
So, the correct answer is (B)

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