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Chapter 6 Class 12 Application of Derivatives
Serial order wise

Ex 6.3, 13 - Find points on x2/9 + y2/16 = 1 at which tangents

Ex 6.3,13 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.3,13 - Chapter 6 Class 12 Application of Derivatives - Part 3 Ex 6.3,13 - Chapter 6 Class 12 Application of Derivatives - Part 4 Ex 6.3,13 - Chapter 6 Class 12 Application of Derivatives - Part 5 Ex 6.3,13 - Chapter 6 Class 12 Application of Derivatives - Part 6 Ex 6.3,13 - Chapter 6 Class 12 Application of Derivatives - Part 7

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Transcript

Question 13 Find points on the curve π‘₯^2/9 + 𝑦^2/16 = 1 at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis. π‘₯^2/9 + 𝑦^2/16 = 1 𝑦^2/16=1βˆ’π‘₯^2/9 Differentiating w.r.t. π‘₯ 𝑑(𝑦^2/16)/𝑑π‘₯=𝑑(1βˆ’ π‘₯^2/9)/𝑑π‘₯ 1/16 𝑑(𝑦^2 )/𝑑π‘₯=𝑑(1)/𝑑π‘₯βˆ’π‘‘(π‘₯^2/9)/𝑑π‘₯ 1/16 Γ— 𝑑(𝑦^2 )/𝑑π‘₯ Γ— 𝑑𝑦/𝑑𝑦=0βˆ’1/9 𝑑(π‘₯^2 )/𝑑π‘₯ 1/16 Γ— 𝑑(𝑦^2 )/𝑑𝑦 Γ— 𝑑𝑦/𝑑π‘₯=(βˆ’ 1)/9 𝑑(π‘₯^2 )/𝑑π‘₯ 1/16 Γ—2𝑦 ×𝑑𝑦/𝑑π‘₯=(βˆ’ 1)/( 9) 2π‘₯ 𝑑𝑦/𝑑π‘₯=((βˆ’ 1)/( 9) 2π‘₯)/(1/16 2𝑦) 𝑑𝑦/𝑑π‘₯=(βˆ’ 16)/9 π‘₯/𝑦 Hence 𝑑𝑦/𝑑π‘₯=(βˆ’ 16)/9 π‘₯/𝑦 parallel to π‘₯βˆ’π‘Žπ‘₯𝑖𝑠 Given tangent is parallel to π‘₯βˆ’π‘Žπ‘₯𝑖𝑠 β‡’ Slope of tangent = Slope of π‘₯βˆ’π‘Žπ‘₯𝑖𝑠 𝑑𝑦/𝑑π‘₯=0 (βˆ’ 16)/( 9) π‘₯/𝑦=0 This is only possible if π‘₯=0 when π‘₯=0 π‘₯^2/4 + 𝑦^2/16=1 0/4+𝑦^2/16=1 (𝐼𝑓 𝑦=0, (βˆ’16)/( 9) π‘₯/0=∞) 𝑦^2/16=1 𝑦^2=16 𝑦=Β±4 Hence the points are (𝟎 , πŸ’) & (𝟎 , βˆ’πŸ’) parallel to π‘¦βˆ’π‘Žπ‘₯𝑖𝑠 Similarly if line is parallel to π‘¦βˆ’π‘Žπ‘₯𝑖𝑠 Angle with π‘₯βˆ’π‘Žπ‘₯𝑖𝑠 =90Β° ΞΈ = 90Β° Slope = tan ΞΈ = tan 90Β°=∞ Hence 𝑑𝑦/𝑑π‘₯=∞ 16/9 π‘₯/𝑦=∞ 16π‘₯/9𝑦=1/0 This will be possible only if Denominator is 0 9𝑦=0 𝑦=0 Now it is given that π‘₯^2/9+𝑦^2/16=1 Putting 𝑦=0 π‘₯^2/9+0/16=1 π‘₯^2/9=1 π‘₯^2=9 π‘₯=√9 π‘₯=Β±3 Hence the points at which tangent is parallel to π‘¦βˆ’π‘Žπ‘₯𝑖𝑠 are (πŸ‘ , 𝟎) & (βˆ’πŸ‘ , 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.