Ex 9.2

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Question 1 Important Deleted for CBSE Board 2025 Exams

Last updated at April 16, 2024 by Teachoo

Ex 9.2, 13 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