Ex 9.3, 5 (i) - Chapter 9 Class 11 Straight Lines

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Ex 9.3, 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 = |𝐶_1− 𝐶_2 |/√(𝐴^2 + 𝐵^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 = − 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 = |𝐶_1− 𝐶_2 |/√(𝐴^2 + 𝐵^2 ) Putting values d = |−34 − 31|/√(〖(15)〗^2 + (8)^2 ) d = |−34 − 31|/√(225 + 64) d = |−65|/√289 d = 65/√(17 × 17) d = 65/17 Thus, the required distance is 𝟔𝟓/𝟏𝟕 units