Question: Consider the conic (5 x^{2}-4 x y+2 y^{2}=30). a. Write the left side in matrix form. b. Diagonalize the coefficient matrix, finding the eigenvalues and

Consider the conic $5 x^{2}-4 x y+2 y^{2}=30$.

a. Write the left side in matrix form.

b. Diagonalize the coefficient matrix, finding the eigenvalues and eigenvectors.

c. Construct the rotation matrix from the information in part $\mathrm{b}$. What is the angle of rotation needed to bring the conic into standard form?

d. What is the conic?

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