Last updated at May 29, 2018 by Teachoo

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Ex10.2, 14 Find equation of the line through the point (0, 2) making an angle 2๐/3 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 2๐/3 with positive x-axis Slope of line AB = tan ฮธ = tan (2๐/3) = tan (120ยฐ) = tan (180 โ 60ยฐ ) = โ tan (60ยฐ) = โ โ3 We know that Equation of line passing through (x0, y0) & having slope m (y โ y0) = m (x โ x0) Equation of line AB passing through (0, 2) & having slope - โ3 (y โ 2) = โ โ3(x โ 0) y โ 2= โ โ3x y + โ3x = 0 + 2 โ3x + y = 2 Hence, equation of line AB is โ3x + y = 2 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, โ2) We know that if two lines are parallel their slopes are equal Therefore , Slope of CD = Slope of AB Slope of CD = โโ3 Now Equation of line passing through point (x0, y0) & having slope m (y โ y0) = m (x โ x0) Equation of line CD passing through (0, -2) & slope โโ3 (y โ (-2)) = โโ3 (x โ 0) (y + 2) = โ3 (x) (y + 2) = โโ3 x y + โ3 x + 2 = 0 โ3 ๐ฅ + y + 2 = 0 Hence equation of line CD = โ3 ๐ฅ + y + 2 = 0

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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.