Question

find the joint equation of the pair of line passing through A(2,3) each of which make angle 30 degree with Y-axis​

Answer 1

Answer:

the point is (2,3)

the angle made with x-axis is 90%-30%=60%

The slope of the line is tan 60%

General equation of line is give as,

y-y1 =m(x-x1)

=> y-3 =√3(x-2)

√3x-y + 3-2√3 = 0

Answer 2

The equation of the line would be

y +√3x = 2√3 + 3

Given

• A(2,3)
• angle 30 degree
• Y-axis

To find

• equation of the pair of line

solution

we are provided with a point and angle that is made between the y axis and the line and are asked to find out the equation of the line which satisfies the given condition.

The equation of a line could be estimated from the slope as well as a point through which it passes.

the angle between the line and the y axis is given as 30 degrees.

Therefore we could estimate the angle between the positive x direction and the line as 120 degrees. ( refer the figure)

now the slope of the line would be,

tan(120) = tan( 180 -60)

or, -tan(60)

or, -√3

the point is given as (2,3)

therefore the equation of the line could be written as (from the point the slope form)

y - 3 = -√3( x - 2)

or, y - 3 = -√3x + 2√3

y +√3x = 2√3 + 3

therefore, the equation of the line would be

y +√3x = 2√3 + 3

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