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Question
The separate equations of the lines represented by `3x^2 - 2sqrt(3)xy - 3y^2` = 0 are ______
Options
`x + sqrt(3)y` = 0 and `sqrt(3)x + y` = 0
`x - sqrt(3)y` = 0 and `sqrt(3)x - y` = 0
`x - sqrt(3)y` = 0 and `sqrt(3)x + y` = 0
`x + sqrt(3)y` = 0 and `sqrt(3)x - y` = 0
Solution
`x - sqrt(3)y` = 0 and `sqrt(3)x + y` = 0
Explanation:
`3x^2 - 2sqrt(3)xy - 3y^2`
Divided by - x2
`(3y^2)/(x^2) + 2sqrt3y/x - 3 = 0`
`3x^2 + 2sqrt3 m - 3 = 0`
quadrant equation
`m = (-2sqrt2+- sqrt12 + 36)/6`
`m = (-2sqrt3 +-sqrt48)/6`
`m = (-2sqrt3 +-4sqrt3)/6`
`m = (-1+-2)/sqrt3` ...(divided by 2√3)
equation of line = y = mx
`y = 1/sqrt3x`
(1) ` sqrt3y - x = 0`
`y = (-3)/sqrt3x`
(2) `sqrt3x + y = 0`
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