Suppose that a quadratic equation in two variables is put into standard form using the following changes of variables: a rotation x = Px' where P is the matrix representing (anticlockwise) rotation by 5*pi/4, and a translation given by x'' = x'+2, y'' = y'-3.

In the new variables x'', y'' it is a parabola with vertex at (0,0) with the x" axis as the axis of symmetry,and which also passed through the point (x",y")=(3,1).

Find the original quadratic equation in terms of x and y. Anyone could give me a hand with this question ? Thanks.

Question

Suppose that a quadratic equation in two variables is put into standard form using the following changes of variables: a rotation x = Px' where P is the matrix representing (anticlockwise) rotation by 5*pi/4, and a translation given by x'' = x'+2, y'' = y'-3.

In the new variables x'', y'' it is a parabola with vertex at (0,0) with the x" axis as the axis of symmetry,and which also passed through the point (x",y")=(3,1).

Find the original quadratic equation in terms of x and y. Anyone could give me a hand with this question ? Thanks.