Question

find the equation of straight lines which makes an angle of 120 degree with positive direction of x axis and passes through the point (0,2)​

Answer 1

we have to find the equation of straight line which makes an angle of 120° with the positive direction of x axis and passes through the point (0,2).

solution : slope of line, m = tanθ

where θ is the angle made by line with the positive direction of x axis.

here θ = 120°

so, tan120° = tan(90° + 30°) = -cot30° = -√3

so slope of line, m = -√3

line is passing through the point (0,2) so equation of line is given by,

(y - 2) = m(x - 0)

⇒y - 2 = -√3x

⇒y + √3x - 2 = 0

⇒√3x + y - 2 = 0

Therefore the equation of line passing through the point (0,2) is √3x + y - 2 = 0.

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Answer 2

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slope of line, m = tanθ

where θ is the angle made by line with the positive direction of x axis.

here θ = 120°

so, tan120° = tan(90° + 30°) = -cot30° = -√3

so slope of line, m = -√3

line is passing through the point (0,2) so equation of line is given by,

(y - 2) = m(x - 0)

⇒y - 2 = -√3x

⇒y + √3x - 2 = 0

⇒√3x + y - 2 = 0

Therefore the equation of line passing through the point (0,2) is √3x + y - 2 = 0.

also read similar questions : Write an equation of the line that passes through the points (−3,−4) and (0,2).

y= [ ]