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Last updated at Feb. 3, 2020 by Teachoo

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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 = |๐ถ_1โ ๐ถ_2 |/โ(๐ด^2 + ๐ต^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 = โ 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 = |๐ถ_1โ ๐ถ_2 |/โ(๐ด^2 + ๐ต^2 ) Putting values d = |โ34 โ 31|/โ(ใ(15)ใ^2 + (8)^2 ) d = |โ34 โ 31|/โ(225 + 64) d = |โ65|/โ289 d = 65/โ(17 ร 17) d = 65/17 Thus, the required distance is ๐๐/๐๐ 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 = |๐ถ_1 โ ๐ถ_2 |/โ(๐ด^2 + ๐ต^2 ) Equation of the first line is ๐(x + y) + p = 0 ๐x + ๐y + 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) โ r = 0 ๐x + ly โ r = 0 The above equation is of the form Ax + By + C2 = 0 where A = ๐ , B = ๐ , C2 = โr Distance between parallel lines ๐(x + y) + p = 0 & ๐(x + y) โ r = 0 is d = |๐ถ_1 โ ๐ถ_2 |/โ(๐ด^2 + ๐ต^2 ) Putting values d = |๐ โ (โ๐)|/โ(๐^2 + ๐^2 ) d = |๐ + ๐|/โ(2๐^2 ) d = (|๐ + ๐| )/(|๐|โ2) d = |(๐ + ๐ )/(๐โ2)| Thus, the required distance is |(๐ + ๐ )/(๐โ๐)| units

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About the Author

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.