6. Consider the function Q(z) = Az[+ B2:1x2+ Cr where A, B, and C are numbers not all zero, = 0 a...
6. Consider the function Q(z) = Az[+ B2:1x2+ Cr where A, B, and C are numbers not all zero, = 0 and the level sets of the associated quadratic form; and recall the well-known classification rule for conic sections by the discriminant (B2 -4AC): if B2 - 4AC < 0, then the conic is an ellipse; if B2-4AC = 0, then the conic is an parabola; and if B2-4AC > 0, then the conic is a hyperbola. (a) Complete the square on Q(x) to remove the x12 term (b) From this, derive the classification rule for conic sections. c) Does the answer depend on how you completed the square? Why or why not? (d) Compute the eigenvalues of the symmetric matrix associated with Q( (e) From this, derive the classification rule for conic sections.
6. Consider the function Q(z) = Az[+ B2:1x2+ Cr where A, B, and C are numbers not all zero, = 0 and the level sets of the associated quadratic form; and recall the well-known classification rule for conic sections by the discriminant (B2 -4AC): if B2 - 4AC 0, then the conic is a hyperbola. (a) Complete the square on Q(x) to remove the x12 term (b) From this, derive the classification rule for conic sections. c) Does the answer depend on how you completed the square? Why or why not? (d) Compute the eigenvalues of the symmetric matrix associated with Q( (e) From this, derive the classification rule for conic sections.