# How do you rotate the axes to transform the equation #4x^2-sqrt3xy+y^2=5# into a new equation with no xy term and then find the angle of rotation?

##### 1 Answer

#### Answer:

Here is a good reference on the topic Rotation of Conic Sections. Please see below.

#### Explanation:

The general Cartesian form for the equation of a conic section is:

Equation [9.4.6] in the reference gives us the angle of rotation:

In given equation,

Note: This is the angle of rotation that makes the

To find the un-rotated value for A, use equation [9.4.4a]:

We know that

To find the un-rotated value for C, use the equation [9.4.4c]:

Equation [9.4.4f] tells us that the constant is unchanged.

Here is the un-rotated equation:

Here is a graph of both equations: