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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


Transcript

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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.