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Example 20 - Find equation of tangent x = a sin3 t , y = b cos3 t - Examples

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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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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 = ﷐𝜋﷮2﷯ . The curve is given as x = a sin3t y = b cos3t Slope of the tangent = ﷐𝑑𝑦﷮𝑑𝑥﷯ ﷐𝑑𝑦﷮𝑑𝑥﷯ = ﷐﷐𝑑𝑦﷮𝑑𝑡﷯﷮﷐𝑑𝑥﷮𝑑𝑡﷯﷯ Hence ﷐𝑑𝑦﷮𝑑𝑥﷯ = ﷐−3𝑏𝑐𝑜﷐𝑠﷮2﷯𝑡﷐sin﷮𝑡﷯﷮3𝑎﷐﷐sin﷮2﷯﷮𝑡﷐cos﷮𝑡﷯﷯﷯ = ﷐−𝑏﷐cos﷮𝑡﷯﷮𝑎﷐sin﷮𝑡﷯﷯ Now, Slope of the tangent at t = ﷐𝜋﷮2﷯ is ﷐﷐﷐𝑑𝑦﷮𝑑𝑥﷯﷯﷮𝑡 = ﷐𝜋﷮ 2﷯﷯ = ﷐−𝑏﷐cos ﷮﷐𝜋﷮2﷯﷯﷮𝑎﷐sin ﷮﷐𝜋﷮2﷯﷯﷯ = ﷐−𝑏(0)﷮𝑎(1)﷯ = 0 Also at t = ﷐𝜋﷮2﷯, 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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