Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

Last updated at Dec. 8, 2016 by Teachoo

Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

Transcript

Example 20 Find the equation of tangent to the curve given by x = a sin3 t , y = b cos3 t at a point where t = 𝜋2 . The curve is given as x = a sin3t y = b cos3t Slope of the tangent = 𝑑𝑦𝑑𝑥 𝑑𝑦𝑑𝑥 = 𝑑𝑦𝑑𝑡𝑑𝑥𝑑𝑡 Hence 𝑑𝑦𝑑𝑥 = −3𝑏𝑐𝑜𝑠2𝑡sin𝑡3𝑎sin2𝑡cos𝑡 = −𝑏cos𝑡𝑎sin𝑡 Now, Slope of the tangent at t = 𝜋2 is 𝑑𝑦𝑑𝑥𝑡 = 𝜋 2 = −𝑏cos 𝜋2𝑎sin 𝜋2 = −𝑏(0)𝑎(1) = 0 Also at t = 𝜋2, value of x and y is Hence, point is (a, 0) Hence, the equation of the tangent at point (𝑎, 0) and with slope 0 is y − 0 = 0 (x − 𝑎) y = 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 9 years. He provides courses for Maths and Science at Teachoo.