$\"\"$

The conic equation is $\"\"$ and angle of rotation is $\"\"$ .

$\"\"$

Rotational formula : $\"\"$ and $\"\"$ .

Substitute $\"\"$ in rotational formulas.

$\"\"$

$\"\"$ .

$\"\"$

$\"\"$ .

Substitute $\"\"$ and $\"\"$ in equation $\"\"$ .

$\"\"$

The equation of the rotated ellipses in the $\"\"$ -plane is $\"\"$ .