Please, help me with this. I have no idea how to solve it
In what points are the tangent to the ellipse parallel to the line y = x?
why are the coefficients written that way?
why not just $\displaystyle 13x^2 - 12xy + 13y^2 = 2$ ?
in any case, find $\displaystyle \frac{dy}{dx}$ implicitly and set it equal to 1.
solve for x in terms of y or y in terms of x (whichever is easier), and sub the result back into the original equation to solve for the that chosen variable.