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If the pair of lines sqrt(3)x^2-4x y+sqr...

If the pair of lines `sqrt(3)x^2-4x y+sqrt(3)y^2=0` is rotated about the origin by `pi/6` in the anticlockwise sense, then find the equation of the pair in the new position.

Text Solution

Verified by Experts

The correct Answer is:
`sqrt(3)x^(2)-xy=0`
The given equation of pair of straight lines can be rewritten as
`(sqrt(3)x-y)(x-sqrt(3y)=0`
Their separate equation are
`y=sqrt(3)xandy=(1)/(sqrt(3))x`
or `y=tan60^(@)xandy=tan 30^(@)x` After rotation , the separate equations are
`y=tan90^(@)xandy=tan 60^(@)x`
or `x=0 and y=sqrt(3)x`
Therefore , the combined equation of lines in the new position is `x(sqrt(3)x-y)=0orsqrt(3)x^(2)-xy=0`
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