Q. 43.9( 76 Votes )

# 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 75^{o}.

Answer :

**Given point = (2, 2√3) and θ = 75°Equation of line: (y - y**

_{1}) = m (x - x

_{1})where, m = slope of line = tan θand (x

_{1}, y

_{1}) are the points through which line passes

∴ m = tan 75°

75° = 45° + 30°

Applying the formula:

Rationalizing we get,

We know that the point (x, y) lies on the line with slope m through the fixed point (x_{1}, y1), if and only if, its coordinates satisfy the equation y – y_{1} = m (x – x_{1})

∴ y – 2√3 = (2 + √3) (x – 2)

⇒ y – 2√3 = 2 x - 4 + √3 x - 2 √3

⇒ y = 2 x - 4 + √3 x

⇒ (2 + √3) x – y - 4 = 0

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

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