Check sibling questions

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

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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.