Question: 10. The equation 5x2 -4ry + 2y2 = 30 describes an ellipse that is rotated by some angle wit to the principal axis. The equation

10. The equation 5x2 -4ry + 2y2 = 30 describes an ellipse that is rotated by some angle wit to the principal axis. The equation written in matrix form will be (x v) (32 20- 30 Find the rotation matrix R such that r = Rr'. Hint: R MR = D where D is diagonal ie diagonalize M by a similarity transformation. Rotating the ellipse to the principal axis will give an equation of the form And" + Azy" = 30. Determine 1.2 and write out the equation in the principal axis

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