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Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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

Β 

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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