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Question

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.

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Solution

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=mx+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=tanθ =tan30° = 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.


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