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  1. Chapter 10 Class 11 Straight Lines
  2. Serial order wise

Transcript

Ex 10.3, 6 Find the distance between parallel lines 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0 We know that , distance between two parallel lines Ax + By + C1 = 0 & Ax + By + C2 = 0 is d = |𝐢_1βˆ’ 𝐢_2 |/√(𝐴^2 + 𝐡^2 ) Equation of first line is 15x + 8y – 34 = 0 Above equation is of the form Ax + By + C1 = 0 where A = 15, B = 8 & C1 = βˆ’ 34 Equation of second line is 15x + 8y + 31 = 0 Above equation is of the form Ax + By + C2 = 0 where A = 15 , B = 8 , C2 = 31 Distance between parallel lines 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0 is d = |𝐢_1βˆ’ 𝐢_2 |/√(𝐴^2 + 𝐡^2 ) Putting values d = |βˆ’34 βˆ’ 31|/√(γ€–(15)γ€—^2 + (8)^2 ) d = |βˆ’34 βˆ’ 31|/√(225 + 64) d = |βˆ’65|/√289 d = 65/√(17 Γ— 17) d = 65/17 Thus, the required distance is πŸ”πŸ“/πŸπŸ• units Ex 10.3, 6 Find the distance between parallel lines (ii) 𝑙(x + y) + p = 0 and 𝑙(x + y) – r = 0 We know that, distance between two parallel lines Ax + By + C1 = 0 & Ax + By + C2 = 0 is d = |𝐢_1 βˆ’ 𝐢_2 |/√(𝐴^2 + 𝐡^2 ) Equation of the first line is 𝑙(x + y) + p = 0 𝑙x + 𝑙y + p = 0 Above equation is of the form Ax + By + C1 = 0 where A = 𝑙 , B = 𝑙 & C1 = p Equation of the second line is 𝑙(x + y) βˆ’ r = 0 𝑙x + ly – r = 0 The above equation is of the form Ax + By + C2 = 0 where A = 𝑙 , B = 𝑙 , C2 = βˆ’r Distance between parallel lines 𝑙(x + y) + p = 0 & 𝑙(x + y) βˆ’ r = 0 is d = |𝐢_1 βˆ’ 𝐢_2 |/√(𝐴^2 + 𝐡^2 ) Putting values d = |𝑝 βˆ’ (βˆ’π‘Ÿ)|/√(𝑙^2 + 𝑙^2 ) d = |𝑝 + π‘Ÿ|/√(2𝑙^2 ) d = (|𝑝 + π‘Ÿ| )/(|𝑙|√2) d = |(𝑝 + π‘Ÿ )/(π‘™βˆš2)| Thus, the required distance is |(𝒑 + 𝒓 )/(π’βˆšπŸ)| units

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.