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 newposition.

If the pair of lines `sqrt(3)x^2-4x y+sqrt(3)y^2=0`is rotated about th

1.	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 newposition.
Answer» Correct Answer - `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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