# Ex 6.3,15

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Ex 6.3,15 Find the equation of the tangent line to the curve 𝑦=𝑥2 −2𝑥+7 which is : (a) parallel to the line 2𝑥−𝑦+9=0 We know that Slope of tangent is 𝑑𝑦𝑑𝑥 𝑦=𝑥2 −2𝑥+7 Differentiating w.r.t.𝑥 𝑑𝑦𝑑𝑥=2𝑥−2 Finding Slope of line 2𝑥−𝑦+9=0 2𝑥−𝑦+9=0 𝑦=2𝑥+9 𝑦=2𝑥+9 The Above Equation is of the form 𝑦=𝑚𝑥+𝑐 where m is Slope of line Hence Slope of line 2𝑥−𝑦+9 is 2 Now, Given tangent is parallel to 2𝑥−𝑦+9=0 Slope of tangent = Slope of line 2𝑥−𝑦+9 = 0 𝑑𝑦𝑑𝑥=2 2𝑥−2=2 2𝑥−1=2 𝑥=2 Finding y when 𝑥=2 , 𝑦=𝑥2−2𝑥+7= 22−22+7=4−4+7=7 We need to find Equation of tangent passes through 2 , 7 & Slope is 2 Equation of tangent is 𝑦−7=2𝑥−2 𝑦−7=2𝑥−4 𝑦−2𝑥−7+4=0 𝑦−2𝑥−3=0 Hence Required Equation of tangent parallel to 𝒚−𝟐𝒙−𝟑=𝟎 Ex 6.3,15 Find the equation of the tangent line to the curve 𝑦=𝑥2−2𝑥+7 which is (b) perpendicular to the line 5𝑦−15𝑥=13 We know that Slope of tangent is 𝑑𝑦𝑑𝑥 𝑦=𝑥2 −2𝑥+7 Differentiating w.r.t.𝑥 𝑑𝑦𝑑𝑥=2𝑥−2 Finding Slope of line 5𝑦−15𝑥=13 5𝑦−15𝑥=13 5𝑦=15𝑥+13 𝑦=1515𝑥+13 𝑦=155𝑥+135 𝑦=3𝑥+135 Above Equation is of the form 𝑦=𝑚𝑥+𝑐 , where m is Slope of a line ∴ Slope = 3 Now, Given tangent is perpendicular to 5𝑦−15𝑥=13 Slope of tangent × Slope of line = –1 𝑑𝑦𝑑𝑥 ×3=−1 𝑑𝑦𝑑𝑥=−1 3 2𝑥−2=−1 3 2𝑥=−1 3+2 2𝑥=−1 + 63 2𝑥=53 𝑥=56 Finding y when 𝑥=56 𝑦=𝑥2−2𝑥+7=562−256+7=2536−106+7=21736 ∴ Point is 56 ,21736 Equation of tangent passing through 56 ,21736 & having Slope −1 3 𝑦−21736=−1 3𝑥−56 36𝑦 −21736=−1 3𝑥−56 36𝑦 −217=−36 3𝑥−5 6 36𝑦 −217=−12𝑥−5 6 36𝑦 −217=−12𝑥+12 × 56 36𝑦 −217=−12𝑥+10 36𝑦 −217=−12𝑥+10 36𝑦+12𝑥−217−10=0 𝟑𝟔𝒚+𝟏𝟐𝒙−𝟐𝟐𝟕=𝟎 is Required Equation of tangent

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Ex 6.3,15 Important You are here

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Ex 6.3,27

Chapter 6 Class 12 Application of Derivatives

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.