NCERT Exemplar - MCQs
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Last updated at Dec. 16, 2024 by Teachoo
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This question is similar to Example 17 - Chapter 6 Class 12 - Application of Derivatives
Transcript
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)
