[" 9.When the axes are rotated an angle "pi/6," find the transformed equation of "],[x^(2)+2sqrt(3)xy-y^(2)=2a^(2)]

When the axes are rotated through an angle pi//6 . Find the transformed equation of x^2+2sqrt3xy-y^2=2a^2 .

When the axes rotated through an angegle (pi)/(4) , find the transformed equation of 3x^2+10xy+3y^2=9 .

When the origin is shifted to (-2,-3) and the axes are rotated through an angle 45^(0) , find the transformed equation of 2x^(2)+4xy-5y^(2)+20x-22y-14 = 0 .

When axes rotated an angle of (pi)/(3) the transformed form of 7x^(2) + 2 sqrt(3) xy + 9y^(2) - 8 = 0 is

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