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Step 1 :

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An equation of the tangent plane to the surface $\"\"$ at the point $\"\"$ is $\"\"$ .

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The equation is $\"\"$ and the point is $\"\"$ .

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Rewrite the equation as z as function in terms of x and y.

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$\"\"$

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Step 2 :

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Let $\"\"$ .

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Apply partial derivative on each side with respect to x.

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$\"\"$

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$\"\"$

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Substitute the point $\"\"$ in above equation.

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$\"\"$

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$\"\"$

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Step 3 :

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The function is $\"\"$ .

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Apply partial derivative on each side with respect to y.

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$\"\"$

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$\"\"$

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Substitute the point $\"\"$ in above equation.

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$\"\"$

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$\"\"$

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Step 4 :

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At the point $\"\"$ , the equation of a tangent plane to the surface is

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$\"\"$ .

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

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$\"\"$

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The equation of a tangent plane to the surface is $\"\"$ .

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Solution :

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The equation of a tangent plane to the surface is $\"\"$ .