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

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  1. Chapter 6 Class 12 Application of Derivatives
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Misc 21 The line = +1 is a tangent to the curve 2 =4 if the value of is (A) 1 (B) 2 (C) 3 (D) 1 2 Let , be the point at which tangent is to be taken & Given Equation of tangent = +1 & Curve is 2 =4 We know that Slope of tangent to the Curve is 2 =4 Differentiating w.r.t. 2 = 4 2 =4 2 =4 2 =4 = 2 Since tangent to be taken from , So, Slope of tangent at , is , = 2 But Given Equation of tangent = +1 Hence Slope of tangent = m = 2 Now, Point , lie on the Curve 2 =4 , will Satisfies the Equation of Curve Putting = , = in equation 2 =4 Also, Point , lie on the tangent , will satisfies the Equation of tangent = +1 Putting = , = in equation = +1 From (1) Putting Value of = 2 = 2 +1 = 2 + 2 =2 + 2 =2 Now Our Equation are 2 =4 (2) 2 =2 (3) Solving (2) 2 =4 2 =2 2 Putting 2 = 2 from (3) 2 =2 2 2 =2 2 2 0=2 2 2 2 2 2 2 2 =0 2 2 =0 2 =0 Hence =0 , 2 Since = not in the Option So, m = 1 Hence Correct Answer is (A)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.