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

(a) 1/2    (b) 1 

(c) 2       (d) 3

 

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

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

Transcript

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 (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’Ž=๐Ÿ So, the correct answer is (B)

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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.