$\"\"$

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Definition of rotation of axes:

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The general second-degree equation $\"\"$ can be

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written as $\"\"$ by rotating the axes by an angle $\"\"$ ,

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where $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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The equation is $\"\"$ .

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Compare the equation $\"\"$ with general equation.

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The values of $\"\"$ , and $\"\"$ .

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$\"\"$

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$\"\"$

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

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Consider $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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$\"\"$

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

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$\"\"$

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The rotated equation is $\"\"$ . $\"\"$

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Graph :

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(1) Draw the coordinate plane.

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(2) Draw the rotated coordinate plane.

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(3) Graph the equation $\"\"$ .

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$\"image\"$

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$\"\"$

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The rotated equation is $\"\"$ .

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Graph of equation $\"\"$ with rotated axis.

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$\"image\"$