1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
  3. NCERT Exemplar - MCQs
Check sibling questions

Question 5 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by Teachoo

The point on the curve y 2 = 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)

 

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œ‹/4 with x-axis is (A) (1/2, 1/4) (B) (1/4, 1/2) (C) (4, 2) (D) (1, 1) 𝑦^2=π‘₯ Slope of the tangent is π’…π’š/𝒅𝒙 Finding π’…π’š/𝒅𝒙 2y 𝑑𝑦/𝑑π‘₯=1 π’…π’š/𝒅𝒙=𝟏/πŸπ’š Since, the tangent makes an angle of πœ‹/4 with x-axis i.e., 𝜽=𝝅/πŸ’ ∴ Slope of tangent =𝒕𝒂𝒏 𝜽 =tanβ‘γ€–πœ‹/4γ€— =𝟏 Equating (1) and (2) 𝟏/πŸπ’š=𝟏 1=2𝑦 2𝑦=1 π’š=𝟏/𝟐 Since, we have to find point on the curve where the tangent makes an angle of πœ‹/4 with x-axis Finding 𝒙 by putting π’š=𝟏/𝟐 in equation of curve π’š^𝟐=𝒙 (𝟏/𝟐)^2=π‘₯ 1/4 =π‘₯ 𝒙=𝟏/πŸ’ ∴ Required point = (x, y) = (𝟏/πŸ’,𝟏/𝟐). So, the correct answer is (B)
  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise

    3. NCERT Exemplar - MCQs

    Tangents and Normals (using Differentiation) →
Tangents and Normals (using Differentiation) →
Chapter 6 Class 12 Application of Derivatives
Serial order wise

About the Author

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo