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Last updated at Feb. 3, 2020 by Teachoo
Ex 10.2, 14 Find equation of the line through the point (0, 2) making an angle 2π/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/3 with positive x-axis Slope of line AB = tan ΞΈ = tan (2π/3) = tan (120Β°) = tan (180 β 60Β° ) = βtan (60Β°) = ββ3 (tan (180 β ΞΈ) = βtan ΞΈ) (tan 60Β° = β3 ) We know that Equation of line passing through (x0, y0) & having slope m (y β y0) = m (x β x0) Equation of line AB passing through (0, 2) & having slope ββ3 (y β 2) = ββ3(x β 0) y β 2= ββ3x y + β3x = 0 + 2 β3x + y = 2 βπx + y β 2 = 0 Hence, equation of line AB is β3x + y β 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, β2) We know that if two lines are parallel their slopes are equal Therefore, Slope of CD = Slope of AB Slope of CD = ββ3 Now Equation of line passing through point (x0, y0) & having slope m (y β y0) = m (x β x0) Equation of line CD passing through (0, -2) & slope ββ3 (y β (β2)) = ββ3 (x β 0) (y + 2) = β3 (x) (y + 2) = ββ3 x y + β3 x + 2 = 0 βπ π + y + 2 = 0 Hence equation of line CD = β3 π₯ + y + 2 = 0