Find the equations of the straight lines passing through the point (2, 1) and making an angle of 45 degrees with the straight line 2x-y+2=0
Answers
Answer:
Let (y+1) = m(x-2) be the st line and tan A = -6/5 slope of given line then
m = tan (A+45) or m= tan(A-45)
case 1) m = (-6/5 +1)(1+6/5) = -1/11
case 2) m = (-6/5–1)/(1–6/5) = 11
Use value of m in (y+1) = m(x-2) to get the lines
Since product of slopes of these lines = -1, they are perpendicular
Answer:
Given: The equation passes through (2, -1) and make an angle of 45° with the line 6x + 5y – 8 = 0 We know that the equations of two lines passing through a point x1, y1 and making an angle α with the given line y = mx + c are Here, equation of the given line is, 6x + 5y – 8 = 0 5y = – 6x + 8 y = -6x/5 + 8/5 Comparing this equation with y = mx + c We get, m = -6/5 Where, x1 = 2, y1 = – 1, α = 45°, m = -6/5 So, the equations of the required lines are x + 11y + 9 = 0 and 11x – y – 23 = 0 ∴ The equation of given line is x + 11y + 9 = 0 and 11x – y – 23 = 0Read more on Sarthaks.com - https://www.sarthaks.com/805111/find-the-equations-straight-lines-passing-through-and-making-an-angle-of-45-with-the-line
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