Last updated at April 19, 2021 by Teachoo

Transcript

Example 16 Find the equation of all lines having slope 2 and being tangent Equation of curve is y + 2/(๐ฅ โ 3) = 0 Differentiating both sides w.r.t x (๐๐ฆ )/๐๐ฅ + (๐ )/๐๐ฅ (2/(๐ฅ โ 3))=0 (๐๐ฆ )/๐๐ฅ =โ(๐ )/๐๐ฅ (2/(๐ฅ โ 3)) (๐๐ฆ )/๐๐ฅ =โ2 (๐ )/๐๐ฅ (๐ฅโ3)^(โ1) (๐๐ฆ )/๐๐ฅ =โ2ใ ร โ(๐ฅโ3)ใ^(โ1โ1) (๐๐ฆ )/๐๐ฅ =2(๐ฅโ3)^(โ2) (๐ ๐ )/๐ ๐ =๐/(๐ โ ๐)^๐ Given that slope = 2 ๐๐ฆ/๐๐ฅ = 2 2/(๐ฅ โ 3)^2 = 2 1/(๐ฅ โ 3)^2 = 1 (๐ฅโ3)^2 = 1 ๐ฅโ3 = ยฑ1 x โ 3 = 1 x = 4 x โ 3 = โ 1 x = 2 x โ 3 = โ 1 x = 2 So, x = 4 & x = 2 Finding value of y If x = 2 y = (โ2)/(๐ฅ โ 3) y = (โ2)/(2 โ 3) ๐ฆ=2 Thus, point is (2, 2) If x = 4 y = (โ2)/(๐ฅ โ 3) y = (โ2)/(4 โ 3) ๐ฆ=โ2 Thus, point is (4, โ2) Thus, there are 2 tangents to the curve with slope 2 and passing through points (2, 2) and (4, โ 2) We know that Equation of line at (๐ฅ1 , ๐ฆ1)& having Slope m is ๐ฆโ๐ฆ1=๐(๐ฅโ๐ฅ1) Equation of tangent through (2, 2) is ๐ฆ โ 2 = 2 (๐ฅ โ2) ๐ฆ โ 2 = 2๐ฅ โ 4 ๐โ๐๐+๐ = ๐ Equation of tangent through (4, โ2) is ๐ฆ โ(โ2) = 2 (๐ฅ โ4) ๐ฆ + 2 = 2๐ฅ โ 8 ๐ โ ๐๐ + ๐๐ = ๐ to the curve y + 2/(๐ฅ โ 3) = 0

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Chapter 6 Class 12 Application of Derivatives

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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.