Question

find the length of the perpendicular from the origin on the lines and the angles made by the perpendicular with the x-axis of the equation √3x + y + 6 = 0​

Answer 1

Answer:

ANSWER

Angle made with positive y-axis =150o

∴ Angle made with positive x-axis =60o

and 180o−60o=120o

Let intercepts made by the line on x & y axis be a & b respectively,

Coordinates are A(a,0) & B(0,b)

Slope =tan120o & slope =tan60o

⇒0−ab−0=−3        ⇒0−ab−0=3

⇒b=a3 ……..(1)          ⇒b=−a3 …….(2)

Equation of line:

y−0=0−ab−0(x−a)

⇒y=−3(x−a) & y=3(x−a)

⇒3x+y−a3=0 & 3