# Help! Rotate the axis to eliminate the xy-term in the equation then write the equation ins standard form. x^2-4xy+4y^2+5sqrt(5)+1=0 Help!?

##### 3 Answers

Please see below.

#### Explanation:

The equation given here

What a rotation does is it changes

In such a case, the relation between coordinate

and reverse is

Note that latter equations are equivalent to rotation by

In such cases, we can eliminate

In given equation we have

or

These two angles relate to

Hence, either

or

and we have

and putting these in given equation and simplifying we get

One can also try for

i.e

and simplifying

**Note** - Please observe that above equation

See below.

#### Explanation:

This possible conic can be written as

Making a coordinate change such that

Choosing

Now substituting this value into the rotation we have

This final result shows that

Please check the original equation. I think there is something wrong.

#### Explanation:

Here is a reference on Rotation of Axes

The general form of a conic is:

For the given equation:

The angle of rotation is:

Using equations from the reference:

I think there is something wrong;

When I try to graph either the original equation or the rotated equation, using Desmos.com, I get nothing.