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For which value of m is the line y = mx + 1 a tangent to the curve y 2 = 4x?

(a) 1/2Β  Β  (b) 1Β 

(c) 2Β  Β  Β  Β (d) 3


This question is inspired from Misc 21 (MCQ) - Chapter 6 Class 12 - Application of Derivatives



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Question 42 For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x? (a) 1/2 (b) 1 (c) 2 (d) 3 Let (β„Ž , π‘˜) be the point at which tangent is to be taken Since (𝒉 , π’Œ) lies on line π‘˜=π‘šβ„Ž+1 Since (𝒉 , π’Œ) lies on curve π‘˜^2=4β„Ž β„Ž=π‘˜^2/4 Putting (2) in (1) π‘˜=π‘š(π’Œ^𝟐/πŸ’)+1 4π‘˜=π‘šπ‘˜^2+4 π‘šπ‘˜^2βˆ’4π‘˜+4=0 Since tangent touches the curve at only one point There is only one value of k So, this quadratic equation has only one root Thus, Discriminant of Quadratic equation = 0 𝒃^πŸβˆ’πŸ’π’‚π’„=𝟎 (βˆ’4)^2βˆ’4 Γ— π‘š Γ— 4=0 16βˆ’16π‘š=0 π‘š=16/16 π’Ž=𝟏 So, the correct answer is (B)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.