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Ex 10.3, 6 - Find distance between parallel lines - Class 11

Ex 10.3, 6 - Chapter 10 Class 11 Straight Lines - Part 2
Ex 10.3, 6 - Chapter 10 Class 11 Straight Lines - Part 3

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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

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