Find the equation of a line, whose inclination is 150° with x-axis an

1.	Find the equation of a line, whose inclination is 150° with x-axis and passes through (3, – 5)
Answer» Inclination of the line, \(\theta\) = 150° ∴ Slope, m = tan(150°) = tan(90° + 60°) = – Cot 60° = – \(\frac{1}{\sqrt{3}}\) Since the line passes through (3, – 5) ∴ Equation of the line is (y – y₀) = m(x – x₀) ⇒ y − (−5) = −\(\frac{1}{\sqrt{3}}\) (x − 3) ⇒ √3(y + 5) = x – 3 ⇒ x + √3y + (5√3 − 3) = 0, is the required equation of the line.

Find the equation of a line, whose inclination is 150° with x-axis and passes through (3, – 5)

Answer»

Inclination of the line, \(\theta\) = 150°

∴ Slope, m = tan(150°) = tan(90° + 60°)

= – Cot 60°

= – \(\frac{1}{\sqrt{3}}\)

Since the line passes through (3, – 5)

∴ Equation of the line is (y – y₀) = m(x – x₀)

⇒ y − (−5) = −\(\frac{1}{\sqrt{3}}\) (x − 3)

⇒ √3(y + 5) = x – 3

⇒ x + √3y + (5√3 − 3) = 0,

is the required equation of the line.