Identify and sketch the graph of the conic described by the quadratic equation x^2 + 4xy + y^2 - 12 = 0. Do this by writing this equation in matrix form; then change the equation to a sum of squares of the form x'^T Dx' where D is a diagonal matrix.
Solution. We can find the matrix of the quadratic form , denoted by A as follows
This shows how to identify and sketch a grph using the matrix form of an equation.