When the axes are rotated through an angle `alpha`, find the transformed equation of `xcos alpha+ysin alpha=p`.

Statement - I : When the axes are rotated through an angle alpha the transformed equation of x cos alpha + y sin alpha = p is X = p Statement - II : A = (2,3), B= (3,5), C = (-1,4) are the vertices of a triangle and the origin is shifted to the point (1,1) then the centroid of the triangle is ((4)/(3),4) Which of the above statement is correct :

When axes rotated through an angle alpha the transformed equation of x cos alpha + y sin alpha = p is

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 are rotated through an angle pi/2 , find the new coordinates of the point (alpha,0)

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