The equation of a curve referred to a given system of axes is `3x^2+2x y+3y^2=10.` Find its equation if the axes are rotated through an angle `45^0` , the origin remaining unchanged.

Explanation

To find the equation of the curve after rotating the axes through an angle of \( 45^\circ \), we will follow these steps:

### Step 1: Define the rotation transformation
When the axes are rotated through an angle \( \theta \), the new coordinates \( x' \) and \( y' \) can be expressed in terms of the original coordinates \( x \) and \( y \) as follows:
\[ x' = x \cos \theta - y \sin \theta \]
\[
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