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Finding the Angle of Rotation

Key Questions

What is does an $x y$ $xy$ term indicate in the equation for a conic section?

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

bp · 2 · Jul 22 2015
How do I find the angle of rotation of a hyperbola?

Answer:

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

Explanation:

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

$A x^{2} + B x y + C y^{2} + D x + E y + F = 0$ $Ax^2 +Bxy+Cy^2 +Dx + Ey +F =0$

Use $cot 2 θ = \frac{A - C}{B}$ $cot2theta = (A-C)/B$ or $tan 2 θ = \frac{B}{A - C}$ $tan2theta = B/(A-C)$ .

Solve for $θ$ $theta$ .

(The $D, E, and F$ $D, E, " and " F$ are not used in the formulas.)

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

Note/Example:
If $A = C$ $A = C$ , then $cot 2 θ = 0$ $cot2theta = 0$ , so $θ = \frac{π}{4}$ $theta = pi/4$

Jim H · 1 · Jul 9 2015

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Translation and Rotation of Axis

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