Problem 4. |24 points] Consider the conic equation with equation-r+6xy-y = 1. a) Identify this equation as a hyperbola or ellipse. b) Find the change of variables = RT conic equation in standard form A1+A2y=1. -1 3 a) The symmetric matrix is A = (7 equation will correspond to a hyperbola. b) The eigenvectors are rotation matrix R (1) ). 3 -1 for -4 and 1/2 -1/2 1/2 1/2 (1/ I needed to "eliminate" the mixed term ry and have the since the eigenvalues are -4, 2, which have opposite sign, the (}) for 2. After normalizing the eigenvectors, we have the so the change of variables is (*) = (+ 1/2 1/2 -1/2 1/2 )(i).