Ex 10.2, 14 - Line through (0, 2) making angle 2pi/3 - Two lines // or/and prependicular

  1. Class 11
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Ex10.2, 14 Find equation of the line through the point (0, 2) making an angle 2๐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 2๐œ‹/3 with positive x-axis Slope of line AB = tan ฮธ = tan (2๐œ‹/3) = tan (120ยฐ) = tan (180 โ€“ 60ยฐ ) = โ€“ tan (60ยฐ) = โ€“ โˆš3 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 - โˆš3 (y โ€“ 2) = โ€“ โˆš3(x โ€“ 0) y โ€“ 2= โ€“ โˆš3x y + โˆš3x = 0 + 2 โˆš3x + y = 2 Hence, equation of line AB is โˆš3x + 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, โ€“2) We know that if two lines are parallel their slopes are equal Therefore , Slope of CD = Slope of AB Slope of CD = โ€“โˆš3 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 โ€“โˆš3 (y โ€“ (-2)) = โ€“โˆš3 (x โ€“ 0) (y + 2) = โˆš3 (x) (y + 2) = โ€“โˆš3 x y + โˆš3 x + 2 = 0 โˆš3 ๐‘ฅ + y + 2 = 0 Hence equation of line CD = โˆš3 ๐‘ฅ + y + 2 = 0

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