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प्रश्न
Given a straight line x cos 30° + y sin 30° = 2. Determine the equation of the other line which is parallel to it and passes through (4, 3).
उत्तर
x cos 30° + y sin 30° = 2
`=> x sqrt(3)/2 + y + 1/2 = 2`
`=> sqrt(3)x + y = 4`
`=> y = -sqrt(3)x + 4`
Slope of this line = `-sqrt(3)`
Slope of a line which is parallel to this given line = `-sqrt(3)`
Let (4, 3) = (x1, y1)
Thus, the equation of the required line is given by :
y – y1 = m(x – x1)
`=> y - 3 = -sqrt(3) (x - 4) = -sqrt(3)x + 4sqrt(3)`
`=> sqrt(3)x + y = 4sqrt(3) + 3`
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