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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​

User Nasir Ali
by
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1 Answer

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Rotating the graph of
Ax^2+Bxy+Cy^2+Dx+Ey+F=0 with
B\\e0 counterclockwise by
\theta eliminates the
xy term, where
\cot2\theta=(A-C)/(B). Plugging in, we have
\cot2\theta=(7)/(24), since
C=0. Solving, we have
\theta=(1)/(2)\cot^(-1)((7)/(24))\approx\boxed{36.9^\circ}.

User Kangasta
by
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