Question

Determine the angle of rotation of the conic section given by: 32x2 +50xy + 7y2 = 100 (round your answer to the nearest tenth of adegree).

Answer 1

The formula to obtain the angle of rotation is as follows:

`\cot 2\theta=(A-C)/(B)`

Compare the given equation to the general equation of a conic.

`Ax^2+Bxy+Cy^2+Dx+Ey+F=0`

Thus, the values of A, B, and C are as follows.

`\begin{gathered} A=32 \\ B=50 \\ C=7 \end{gathered}`

Substitute the values into the equation.

`\begin{gathered} \cot 2\theta=(32-7)/(50) \\ \cot 2\theta=(25)/(50) \\ \cot 2\theta=(1)/(2) \end{gathered}`

Find the value of the θ.

`\begin{gathered} (1)/(\tan 2\theta)=(1)/(2) \\ \tan 2\theta=2 \\ 2\theta=\tan ^(-1)(2) \\ 2\theta\approx63.4349 \\ \theta\approx31.7 \end{gathered}`