Example 17 - Find points on x2/4 + y2/25 = 1 at which tangents - Finding point when tangent is parallel/ perpendicular

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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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Example 17 Find points on the curve ﷐﷐𝑥﷮2﷯﷮4﷯ + ﷐﷐𝑦﷮2﷯﷮25﷯ = 1 at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis. The curve is ﷐﷐𝑥﷮2﷯﷮4﷯ + ﷐﷐𝑦﷮2﷯﷮25﷯ = 1 Slope of x axis = 0 Slope of y axis = ﷐1﷮0﷯ Slope of the tangent is ﷐𝑑𝑦﷮𝑑𝑥﷯ Finding ﷐𝒅𝒚﷮𝒅𝒙﷯ ﷐2𝑥﷮4﷯+﷐2𝑦 ﷐𝑑𝑦﷮𝑑𝑥﷯﷮25﷯ = 0 ﷐𝑥﷮2﷯ + ﷐2𝑦﷮25﷯﷐𝑑𝑦﷮𝑑𝑥﷯ = 0 ⇒ ﷐𝑑𝑦﷮𝑑𝑥﷯ = ﷐−𝑥﷮2﷯ × ﷐25﷮2𝑦﷯ = ﷐−25𝑥﷮4𝑦﷯ Hence ﷐𝑑𝑦﷮𝑑𝑥﷯ = −﷐−25𝑥﷮4𝑦﷯ (1) If the tangent is parallel to x – axis, its slope is 0 Hence ﷐𝑑𝑦﷮𝑑𝑥﷯ = 0 ﷐−25𝑥﷮4𝑦﷯ = 0 x = 0 Putting this in equation of the curve ﷐0﷮4﷯ + ﷐﷐𝑦﷮2﷯﷮25﷯ = 1 ﷐𝑦﷮2﷯ = 25 y = ± 5 Hence, the points are (0, 5) and (0, −5) (2) If the tangent is parallel to y − axis, its slope is 1/0 Hence ﷐𝑑𝑦﷮𝑑𝑥﷯ = ﷐1﷮0﷯ ﷐−25𝑥﷮4𝑦﷯ = ﷐1﷮0﷯ y = 0 Putting this in equation of the curve ﷐﷐𝑥﷮2﷯﷮4﷯ + ﷐0﷮25﷯ = 1 x = 4 x = ± 2 Hence, the points are (2, 0) and (−2, 0)

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