# Example 20 - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

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.