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

  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

Transcript

Misc 21 The line ๐‘ฆ=๐‘š๐‘ฅ+1 is a tangent to the curve ๐‘ฆ^2=4๐‘ฅ if the value of ๐‘š is (A) 1 (B) 2 (C) 3 (D) 1/2Let (โ„Ž , ๐‘˜) be the point at which tangent is to be taken & Given Equation of tangent ๐‘ฆ=๐‘š๐‘ฅ+1 & Curve is ๐‘ฆ^2=4๐‘ฅ We know that Slope of tangent to the Curve is ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ ๐‘ฆ^2=4๐‘ฅ Misc 21 The line ๐‘ฆ=๐‘š๐‘ฅ+1 is a tangent to the curve ๐‘ฆ^2=4๐‘ฅ if the value of ๐‘š is (A) 1 (B) 2 (C) 3 (D) 1/2Let (โ„Ž , ๐‘˜) be the point at which tangent is to be taken Since (๐’‰ , ๐’Œ) lies on line ๐‘˜=๐‘šโ„Ž+1 Since (๐’‰ , ๐’Œ) lies on curve ๐‘˜^2=4โ„Ž โ„Ž=๐‘˜^2/4 Putting (2) in (1) ๐‘˜=๐‘š(๐’Œ^๐Ÿ/๐Ÿ’)+1 4๐‘˜=๐‘š๐‘˜^2+4 ๐‘š๐‘˜^2โˆ’4๐‘˜+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 ๐’ƒ^๐Ÿโˆ’๐Ÿ’๐’‚๐’„=๐ŸŽ (โˆ’4)^2โˆ’4 ร— ๐‘š ร— 4=0 16โˆ’16๐‘š=0 ๐‘š=16/16 ๐‘š=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 10 years. He provides courses for Maths and Science at Teachoo.