Example 17 - Find points on x2/4 + y2/25 = 1 at which tangents

Example 17 - Chapter 6 Class 12 Application of Derivatives - Part 2
Example 17 - Chapter 6 Class 12 Application of Derivatives - Part 3 Example 17 - Chapter 6 Class 12 Application of Derivatives - Part 4 Example 17 - Chapter 6 Class 12 Application of Derivatives - Part 5 Example 17 - Chapter 6 Class 12 Application of Derivatives - Part 6

  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

Transcript

Example 17 Find points on the curve π‘₯^2/4 + 𝑦^2/25 = 1 at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis.Given curve π‘₯^2/4 + 𝑦^2/25 = 1 Slope of the tangent is 𝑑𝑦/𝑑π‘₯ Finding π’…π’š/𝒅𝒙 2π‘₯/4+(2𝑦 )/25 Γ— 𝑑𝑦/𝑑π‘₯= 0 π‘₯/2 + 2𝑦/25 𝑑𝑦/𝑑π‘₯ = 0 2𝑦/25 𝑑𝑦/𝑑π‘₯ = (βˆ’π‘₯)/2 𝑑𝑦/𝑑π‘₯ = (βˆ’π‘₯)/2 Γ— 25/2𝑦 π’…π’š/𝒅𝒙 = (βˆ’πŸπŸ“π’™)/πŸ’π’š Hence, 𝑑𝑦/𝑑π‘₯ = βˆ’ (βˆ’25π‘₯)/4𝑦 (i) Tangent is parallel to x-axis If the tangent is parallel to x-axis, its slope is 0 Hence, 𝑑𝑦/𝑑π‘₯ = 0 (βˆ’25π‘₯)/4𝑦 = 0 x = 0 Putting x = 0 in equation of the curve π‘₯^2/4 + 𝑦^2/25 = 1 0/4 + 𝑦^2/25 = 1 𝑦^2 = 25 y = Β± 5 Hence, the points are (0, 5) and (0, βˆ’5) (ii) Tangent is parallel to y-axis If the tangent is parallel to y-axis, its slope is 1/0 Hence, 𝑑𝑦/𝑑π‘₯ = 1/0 (βˆ’25π‘₯)/4𝑦 = 1/0 y = 0 Putting y = 0 in equation of the curve π‘₯^2/4 + 𝑦^2/25 = 1 π‘₯^2/4 + 0/25 = 1 π‘₯^2/4 = 1 x2 = 4 x = Β± 2 Hence, the points are (2, 0) and (βˆ’2, 0)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.