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Ex 10.2, 14 - Line through (0, 2) making angle 2pi/3 - Ex 10.2

Ex 10.2, 14 - Chapter 10 Class 11 Straight Lines - Part 2
Ex 10.2, 14 - Chapter 10 Class 11 Straight Lines - Part 3 Ex 10.2, 14 - Chapter 10 Class 11 Straight Lines - Part 4

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Ex 10.2, 14 Find equation of the line through the point (0, 2) making an angle 2πœ‹/3 with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin. Let AB be the line passing through P(0, 2) & making an angle 2πœ‹/3 with positive x-axis Slope of line AB = tan ΞΈ = tan (2πœ‹/3) = tan (120Β°) = tan (180 – 60Β° ) = –tan (60Β°) = β€“βˆš3 (tan (180 – ΞΈ) = –tan ΞΈ) (tan 60Β° = √3 ) We know that Equation of line passing through (x0, y0) & having slope m (y – y0) = m (x – x0) Equation of line AB passing through (0, 2) & having slope βˆ’βˆš3 (y – 2) = β€“βˆš3(x – 0) y – 2= β€“βˆš3x y + √3x = 0 + 2 √3x + y = 2 βˆšπŸ‘x + y βˆ’ 2 = 0 Hence, equation of line AB is √3x + y βˆ’ 2 = 0 Also, we have to find equation of line which is parallel to line AB & crossing at a distance of 2 unit below the origin Let CD be the line parallel to AB & passing through point R(0, –2) We know that if two lines are parallel their slopes are equal Therefore, Slope of CD = Slope of AB Slope of CD = β€“βˆš3 Now Equation of line passing through point (x0, y0) & having slope m (y – y0) = m (x – x0) Equation of line CD passing through (0, -2) & slope β€“βˆš3 (y – (βˆ’2)) = β€“βˆš3 (x – 0) (y + 2) = √3 (x) (y + 2) = β€“βˆš3 x y + √3 x + 2 = 0 βˆšπŸ‘ 𝒙 + y + 2 = 0 Hence equation of line CD = √3 π‘₯ + y + 2 = 0

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.