Find the equation of the line which intersects the y -axis at a distance of 2 units above the origin and makes an angle of 30° with the positive direction of the x -axis.
The line intersects the y-axis at a distance of two units above the origin and the line making an angle of 30 ° with positive direction of the x-axis.
Let, c be the intercept formed by the line having slope m .
The formula for the line with slope m having an intercept c on y-axis is given by,
y = m x + c (1)
The formula for the slope m of a line subtends an angle θ in anticlockwise direction with positive x-axis is given by,
m = tan θ = tan 30 ° = 1 3
Substitute the value of m in equation (1).
y = 1 3 x + c (2)
Since the line intersecting above the origin makes an intercept y-axis.
According to question the line intersects above 2 units the y-axis.
c = 2
Substitute the value of c in equation (2).
y = 1 3 x + 2 3 y = x + 2 3 x − 3 y + 2 3 = 0
Thus, the equation of line intersects at a distance of two units above origin and makes an angle of 30 ° is x − 3 y + 2 3 = 0 .
The line intersects the y-axis at a distance of two units above the origin and the line making an angle of
Let,
The formula for the line with slope
The formula for the slope m of a line subtends an angle
Substitute the value of m in equation (1).
Since the line intersecting above the origin makes an intercept y-axis.
According to question the line intersects above 2 units the y-axis.
Substitute the value of
Thus, the equation of line intersects at a distance of two units above origin and makes an angle of
