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Ex 6.3, 22 - Find equations of tangent and normal to parabola - Finding equation of tangent/normal when point and curve is given

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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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Ex 6.3,22 Find the equations of the tangent and normal to the parabola ﷐𝑦﷮2﷯=4𝑎𝑥 at the point (𝑎𝑡2, 2𝑎𝑡). Given Curve is ﷐𝑦﷮2﷯=4𝑎𝑥 We need to find equation of tangent & Normal at (𝑎𝑡2, 2𝑎𝑡) We know that Slope of tangent is ﷐𝑑𝑦﷮𝑑𝑥﷯ ﷐𝑦﷮2﷯=4𝑎𝑥 Differentiating w.r.t.𝑥 ﷐𝑑﷐﷐𝑦﷮2﷯﷯﷮𝑑𝑥﷯=﷐𝑑﷐4𝑎𝑥﷯﷮𝑑𝑥﷯ ﷐𝑑﷐﷐𝑦﷮2﷯﷯﷮𝑑𝑥﷯ × ﷐𝑑𝑦﷮𝑑𝑦﷯=4𝑎﷐𝑑﷐𝑥﷯﷮𝑑𝑥﷯ ﷐𝑑﷐﷐𝑦﷮2﷯﷯﷮𝑑𝑦﷯ × ﷐𝑑𝑦﷮𝑑𝑥﷯=4𝑎 2𝑦 ×﷐𝑑𝑦﷮𝑑𝑥﷯=4𝑎 ﷐𝑑𝑦﷮𝑑𝑥﷯=﷐4𝑎﷮2𝑦﷯ Slope of tangent at ﷐𝑎﷐𝑡﷮2﷯ , 2𝑎𝑡﷯ is ﷐﷐𝑑𝑦﷮𝑑𝑥﷯│﷮﷐𝑎﷐𝑡﷮2﷯ , 2𝑎𝑡﷯﷯=﷐4𝑎﷮2﷐2𝑎𝑡﷯﷯=﷐4𝑎﷮4𝑎𝑡﷯=﷐1﷮𝑡﷯ Also we know that Slope of tangent × Slope of Normal =−1 ﷐1﷮𝑡﷯× Slope of Normal =−1 Slope of Normal =﷐−1﷮ ﷐1﷮𝑡﷯﷯ Finding equation of tangent & normal

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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