Ex 10.3, 6

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Ex10.3, 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 ) 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 Ex10.3, 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 = |𝐶_1 − 𝐶_2 |/√(𝐴^2 + 𝐵^2 ) Distance between parallel lines 𝑙(x + y) + p = 0 & 𝑙(x + y) − r = 0 is d = |𝐶_1 − 𝐶_2 |/√(𝐴^2 + 𝐵^2 ) Putting values d = |𝑝 − ( − 𝑟)|/√(𝑙^2 + 𝑙^2 ) d = |𝑝 + 𝑟|/√(2𝑙^2 ) d = (𝑝 + 𝑟 )/(𝑙√2) Thus, the required distance is (𝑝 + 𝑟 )/(𝑙√2) units