In Exercises, find the equation of the line which satisfy the given conditions:

Passing through and inclined with the x-axis at an angle of 75o.


Given point = (2, 2√3) and θ = 75°


We know that m = tanθ


m = tan75° = 2 + 3


We know that the point (x, y) lies on the line with slope m through the fixed point (x0, y0), if and only if, its coordinates satisfy the equation y – y0 = m (x – x0)


y 23 = (2 + √3) (x – 2)


y 23 = (2 + 3) x + 4 23


(2 + 3) x – y + 4 – 2√3 + 2√3 = 0


(2 + 3) x y + 4 = 0


Ans. The equation of the line is (2 + √3) x – y + 4 = 0.


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