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myrzilka [38]
3 years ago
7

Find in degrees the numeric value of the acute angle of rotation that eliminates the product term from the equation 7x2+24xy−34x

+24y−185=07x2+24xy−34x+24y−185=0​
Mathematics
1 answer:
lutik1710 [3]3 years ago
4 0

Rotating the graph of Ax^2+Bxy+Cy^2+Dx+Ey+F=0 with B\ne0 counterclockwise by \theta eliminates the xy term, where \cot2\theta=\frac{A-C}{B}. Plugging in, we have \cot2\theta=\frac{7}{24}, since C=0. Solving, we have \theta=\frac{1}{2}\cot^{-1}(\frac{7}{24})\approx\boxed{36.9^\circ}.

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