Last updated at April 19, 2021 by Teachoo

Transcript

Misc 21 The line ๐ฆ=๐๐ฅ+1 is a tangent to the curve ๐ฆ^2=4๐ฅ if the value of ๐ is (A) 1 (B) 2 (C) 3 (D) 1/2Let (โ , ๐) be the point at which tangent is to be taken & Given Equation of tangent ๐ฆ=๐๐ฅ+1 & Curve is ๐ฆ^2=4๐ฅ We know that Slope of tangent to the Curve is ๐๐ฆ/๐๐ฅ ๐ฆ^2=4๐ฅ Misc 21 The line ๐ฆ=๐๐ฅ+1 is a tangent to the curve ๐ฆ^2=4๐ฅ if the value of ๐ is (A) 1 (B) 2 (C) 3 (D) 1/2Let (โ , ๐) be the point at which tangent is to be taken Since (๐ , ๐) lies on line ๐=๐โ+1 Since (๐ , ๐) lies on curve ๐^2=4โ โ=๐^2/4 Putting (2) in (1) ๐=๐(๐^๐/๐)+1 4๐=๐๐^2+4 ๐๐^2โ4๐+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 ๐^๐โ๐๐๐=๐ (โ4)^2โ4 ร ๐ ร 4=0 16โ16๐=0 ๐=16/16 ๐=1 Hence Correct Answer is (A)

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About the Author

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.