solve the problem

2. Consider the quadratic form f(x,y) = x2 + xy +y?. (a) [3 points] Show that the form f is positive by showing that the corresponding symmetric matrix S, such that, f(x, y) = [x y] s is positive definite. (b) [7 points] Draw the tilted ellipse x2 + ry + y? = 1, find the axes and the half-lengths of its axes from the eigenvectors and eigenvalues of the corresponding matrix S