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Problem 4 24 points Consider the conic equation with equation 7 6ry y 1 a...

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Algebra

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Problem 4 24 points Consider the conic equation with equation 7 6ry y 1 a Identify this equation as a hyperbola or ellipse b Find the change of variables RT needed to eliminate the mixed term ry and have the conic equation in standard form A a The symmetric matrix is A equation will correspond to a hyperbola b The eigenvectors are 1 2 1 2 1 2 1 2 rotation matrix R A y2 1 1 3 s since the eigenvalues are 4 2 which have opposite sign the 3 1 for 4 and 1 for 2 After normalizing the eigenvectors we have the 1 2 1 2 1 2 1 V so the change of variables is

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