If the transformed equation of a curve is `X^(2) + 2 sqrt(3) XY - Y^(2) =2 a^(2)` when the axes are rotated through angle `60^(0)`, then find the original equation of the curve.

If the transferred equation of a curve is x^(2) + 2sqrt(3)xy - y^(2) = 2a^(2) when the axes are rotated through an angle 60^(@) , then the original equation of the curve is

If the transformed equation of a curve is X^(2) - 2XY tan 2 alpha - Y^(2) = a^(2) when the axes are rotated through an angle alpha , then the original equation of the curve is

Find the transformed equation of x^(2) + 2 sqrt(3) xy - y^(2) = 2a^(2) when the axes are rotated through an angle 30^(0)

If the transformed equation of curve is 17X^(2) - 16XY + 17y^(2) = 225 when the axes are rotated through an angle 45^(0) , then the original equation of the curve is

The transformed equation of x^(2) - 2sqrt(3)xy -y^(2) =2a^(2) when the axes are rotated through an angle 60^(@) is

If the transformed equation of a curve is X^(2) + 3XY - 2Y^(2) + 17X - 7Y - 11 = 0 when the axes are translated to the point (2,3) then find the original equation of the curve.

If the transformed equation of a curve is 17x^(2) - 16xy + 17y^(2)=225 when the axes are rotated through an angle 45^(@) , then the original equation of the curve is

If the transformed equation of a curve is 3X^(2) + XY - Y^(2)- 7X + Y +7=0 when the axes are translated to the point (1,2), then the original equation of the curve is 3x^(2) + xy - y^(2) -ax + by+c=0 , then the ascending order of a,b,c is

Find the transformed equation of x^(2)+2sqrt3 xy-y^(2) = 2a^(2) when the axes are rotated through an angle 30^(0).