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Misc 21 - Line y = mx + 1 is tangent to y2 = 4x if value of m is

Misc 21 - Chapter 6 Class 12 Application of Derivatives - Part 2
Misc 21 - Chapter 6 Class 12 Application of Derivatives - Part 3
Misc 21 - Chapter 6 Class 12 Application of Derivatives - Part 4

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Misc 21 The line 𝑦=𝑚𝑥+1 is a tangent to the curve 𝑦^2=4𝑥 if the value of 𝑚 is (A) 1 (B) 2 (C) 3 (D) 1/2Let (ℎ , 𝑘) be the point at which tangent is to be taken & Given Equation of tangent 𝑦=𝑚𝑥+1 & Curve is 𝑦^2=4𝑥 We know that Slope of tangent to the Curve is 𝑑𝑦/𝑑𝑥 𝑦^2=4𝑥 Misc 21 The line 𝑦=𝑚𝑥+1 is a tangent to the curve 𝑦^2=4𝑥 if the value of 𝑚 is (A) 1 (B) 2 (C) 3 (D) 1/2Let (ℎ , 𝑘) be the point at which tangent is to be taken Since (𝒉 , 𝒌) lies on line 𝑘=𝑚ℎ+1 Since (𝒉 , 𝒌) lies on curve 𝑘^2=4ℎ ℎ=𝑘^2/4 Putting (2) in (1) 𝑘=𝑚(𝒌^𝟐/𝟒)+1 4𝑘=𝑚𝑘^2+4 𝑚𝑘^2−4𝑘+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^𝟐−𝟒𝒂𝒄=𝟎 (−4)^2−4 × 𝑚 × 4=0 16−16𝑚=0 𝑚=16/16 𝑚=1 Hence Correct Answer is (A)

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.