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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 โ€“ 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 = |๐ถ_1โˆ’ ๐ถ_2 |/โˆš(๐ด^2 + ๐ต^2 ) Equation of first line is 15x + 8y โ€“ 34 = 0 Above equation is of the form Ax + By + C1 = 0 where A = 15, B = 8 & C1 = โˆ’ 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 โ€“ 34 = 0 and 15x + 8y + 31 = 0 is d = |๐ถ_1โˆ’ ๐ถ_2 |/โˆš(๐ด^2 + ๐ต^2 ) Putting values d = |โˆ’34 โˆ’ 31|/โˆš(ใ€–(15)ใ€—^2 + (8)^2 ) d = |โˆ’34 โˆ’ 31|/โˆš(225 + 64) d = |โˆ’65|/โˆš289 d = 65/โˆš(17 ร— 17) d = 65/17 Thus, the required distance is ๐Ÿ”๐Ÿ“/๐Ÿ๐Ÿ• units Ex 10.3, 6 Find the distance between parallel lines (ii) ๐‘™(x + y) + p = 0 and ๐‘™(x + y) โ€“ r = 0 We know that, distance between two parallel lines Ax + By + C1 = 0 & Ax + By + C2 = 0 is d = |๐ถ_1 โˆ’ ๐ถ_2 |/โˆš(๐ด^2 + ๐ต^2 ) Equation of the first line is ๐‘™(x + y) + p = 0 ๐‘™x + ๐‘™y + p = 0 Above equation is of the form Ax + By + C1 = 0 where A = ๐‘™ , B = ๐‘™ & C1 = p Equation of the second line is ๐‘™(x + y) โˆ’ r = 0 ๐‘™x + ly โ€“ r = 0 The above equation is of the form Ax + By + C2 = 0 where A = ๐‘™ , B = ๐‘™ , C2 = โˆ’r Distance between parallel lines ๐‘™(x + y) + p = 0 & ๐‘™(x + y) โˆ’ r = 0 is d = |๐ถ_1 โˆ’ ๐ถ_2 |/โˆš(๐ด^2 + ๐ต^2 ) Putting values d = |๐‘ โˆ’ (โˆ’๐‘Ÿ)|/โˆš(๐‘™^2 + ๐‘™^2 ) d = |๐‘ + ๐‘Ÿ|/โˆš(2๐‘™^2 ) d = (|๐‘ + ๐‘Ÿ| )/(|๐‘™|โˆš2) d = |(๐‘ + ๐‘Ÿ )/(๐‘™โˆš2)| Thus, the required distance is |(๐’‘ + ๐’“ )/(๐’โˆš๐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.