Question 4 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives

Last updated at April 16, 2024 by

The equation of the normal to the curve y = sin x at (0, 0) is:

(A)x = 0                  (B) y = 0

(C) x + y = 0           (D) x – y = 0

 

This question is similar to Ex 6.3, 14 (i) - Chapter 6 Class 12 - Application of Derivatives

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Question 4 The equation of the normal to the curve y = sin x at (0, 0) is: x = 0 (B) y = 0 (C) x + y = 0 (D) x – y = 0 𝑦=sin⁑π‘₯ Since Slope of normal =(βˆ’1)/(𝑑𝑦/𝑑π‘₯) Differentiating 𝑦 w.r.t. π‘₯ 𝑑𝑦/𝑑π‘₯=πœπ¨π¬β‘π’™ Since given point is (0, 0) Putting 𝒙=𝟎 in (1) π’…π’š/𝒅𝒙 =cos⁑0 𝑑𝑦/𝑑π‘₯=𝟏 Hence, Slope of normal =(βˆ’1)/(𝑑𝑦/𝑑π‘₯) =(βˆ’1)/1 =βˆ’πŸ Finding equation of normal Equation of line at (π‘₯1 , 𝑦1) & having Slope m is π‘¦βˆ’π‘¦1=π‘š(π‘₯βˆ’π‘₯1) ∴ Equation of Normal at (0, 0) & Slope -1 is (π’šβˆ’πŸŽ)=βˆ’πŸ(π’™βˆ’πŸŽ) 𝑦=βˆ’1(π‘₯) 𝑦=βˆ’π‘₯ π’š+𝒙=𝟎 Hence, equation of normal is π’š+𝒙=𝟎 So, the correct answer is (C)

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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