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Question
Find the equation of line through the intersection of lines 2x – y = 1 and 3x + 2y = –9 and making an angle of 30° with positive direction of x-axis.
Solution
Since the line passing through the x-axis makes an angle of 30° with the positive direction of the x-axis.
The slope of the line is given by tan `30^circ = 1/sqrt(3)`
The intersection of the lines 2x – y = 1 and 3x + 2y = –9 is given by solving the equation simultaneously.
So, multiplying equation 2x – y = 1 by 2, we get
4x – 2y = 2
Now add this resulting to the second equation 3x + 2y = –9
`=>` 7x = –7
`=>` x = –1
Substituting the value of x ∈ 2x – y = 1, we get
y = –3
Thus, the intersection of the lines is (–1, –3).
To find the equation of the required line,
We use the slope-point form, so we get
`y - (-3) = 1/sqrt(3)[x - (1)]`
i.e. `y + 3 = 1/sqrt(3)(x + 1)`
i.e `y = x/sqrt(3) + 1/sqrt(3) - 3`
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