If we rewrite the general equation of degree 2 (Eq. 12) in terms of variables x and y

Chapter 11, Problem 76

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If we rewrite the general equation of degree 2 (Eq. 12) in terms of variables x and y that are related to x and y by Eqs. (13) and (14), we obtain a new equation of degree 2 in x and y of the same form but with different coefficients: a x2 + b xy + c y 2 + d x + e y + f = 0 (a) Show that b = b cos 2 + (c a)sin 2. (b) Show that if b = 0, then we obtain b = 0 for = 1 2 cot1 a c b This proves that it is always possible to eliminate the cross term bxy by rotating the axes through a suitable angle. CHAPTE