Example 16 - Find equation of all lines having slope 2, tangent - Examples

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  1. Chapter 6 Class 12 Application of Derivatives
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Example 16 Find the equation of all lines having slope 2 and being tangent to the curve y + ﷐2﷮𝑥 − 3﷯ = 0 The curve is y + ﷐2﷮𝑥−3﷯ = 0 Slope of the tangent to the curve at point (x, y) is ﷐𝑑𝑦 ﷮𝑑𝑥﷯ ﷐𝑑𝑦 ﷮𝑑𝑥﷯ + ﷐𝑑 ﷮𝑑𝑥﷯﷐﷐2﷮𝑥 − 3﷯﷯=0 ﷐𝑑𝑦 ﷮𝑑𝑥﷯ =− ﷐𝑑 ﷮𝑑𝑥﷯﷐﷐2﷮𝑥 − 3﷯﷯ ﷐𝑑𝑦 ﷮𝑑𝑥﷯ =− ﷐﷐0﷐𝑥 − 3﷯ − 2﷐1﷯﷮﷐﷐𝑥 − 3﷯﷮2﷯﷯﷯ ﷐𝑑𝑦 ﷮𝑑𝑥﷯ =− ﷐﷐−2﷮﷐﷐𝑥 − 3﷯﷮2﷯﷯﷯ ﷐𝑑𝑦 ﷮𝑑𝑥﷯ =﷐2﷮﷐﷐𝑥 − 3﷯﷮2﷯﷯ Given that slope = 2 Hence, ﷐𝑑𝑦﷮𝑑𝑥﷯ = 2 ﷐2﷮﷐﷐𝑥 − 3﷯﷮2﷯﷯=2 ﷐1﷮﷐﷐𝑥 − 3﷯﷮2﷯﷯=1 ﷐﷐𝑥−3﷯﷮2﷯ = 1 So, x – 3 = ±1 So, x = 4 & x = 2 Finding value of y Thus, there are 2 tangents to the curve with slope 2 and passing through points (2, 2) and (4, − 2)

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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.