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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1
Fig: 1