Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12      1. Chapter 6 Class 12 Application of Derivatives
2. Serial order wise
3. Examples

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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. Given curve 𝑥^2/4 + 𝑦^2/25 = 1 Slope of the tangent is 𝑑𝑦/𝑑𝑥 Finding 𝒅𝒚/𝒅𝒙 2𝑥/4+(2𝑦 𝑑𝑦/𝑑𝑥)/25 = 0 𝑥/2 + 2𝑦/25 𝑑𝑦/𝑑𝑥 = 0 2𝑦/25 𝑑𝑦/𝑑𝑥 = (−𝑥)/2 𝑑𝑦/𝑑𝑥 = (−𝑥)/2 × 25/2𝑦 𝑑𝑦/𝑑𝑥 = (−25𝑥)/4𝑦 Hence, 𝑑𝑦/𝑑𝑥 = − (−25𝑥)/4𝑦 (i) Tangent is parallel to x-axis If the tangent is parallel to x – axis, its slope is 0 Hence, 𝑑𝑦/𝑑𝑥 = 0 (−25𝑥)/4𝑦 = 0 x = 0 Putting x = 0 in equation of the curve 𝑥^2/4 + 𝑦^2/25 = 1 0/4 + 𝑦^2/25 = 1 𝑦^2 = 25 y = ± 5 Hence, the points are (0, 5) and (0, −5) (ii) Tangent is parallel to y-axis 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 y = 0 in equation of the curve 𝑥^2/4 + 𝑦^2/25 = 1 𝑥^2/4 + 0/25 = 1 𝑥^2/4 = 1 x2 = 4 x = ± 2 Hence, the points are (2, 0) and (−2, 0)

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