Question

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​

Answer 1

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}.`