# Finding the Angle of Rotation

## Key Questions

• xy term in the equation of a conic section indicates, there is a rotation of axes

Use a formula and solve for angle of rotation = $\theta$

#### Explanation:

For the formulas I use, we must put the equation in the form:

$A {x}^{2} + B x y + C {y}^{2} + D x + E y + F = 0$

Use $\cot 2 \theta = \frac{A - C}{B}$ or $\tan 2 \theta = \frac{B}{A - C}$.

Solve for $\theta$.

(The $D , E , \text{ and } F$ are not used in the formulas.)

Your textbook/teacher may prefer a different form, which would lead to different formulas.

Note/Example:
If $A = C$, then $\cot 2 \theta = 0$, so $\theta = \frac{\pi}{4}$