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3. Assuming the ellipsoid E2 is such that

E₂ = {x= [x, y]: 13x² +10xy+13y² = 72, x € R, y ≤ R}

a) Show that

13x² + 10ry + 13y² = 72 if and only if

for some a, b, u, and v

b) Derive the principal axes of E2. Find their respective lengths.

c) Plot the ellipsoid and the principal axes.

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Fig: 1