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Step 1 :

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The equation of a tangent plane :

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The tangent plane equation at the point $\"\"$ is

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$\"\"$

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The normal line to the surface at the point $\"\"$ is

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$\"\"$

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Step 2 :

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(a)

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

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Rewrite the equation as $\"\"$ .

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Consider $\"\"$ .

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Differentiate $\"\"$ partially with respect to $\"\"$ .

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$\"\"$

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

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$\"\"$ .

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Differentiate $\"\"$ partially with respect to $\"\"$ .

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$\"\"$

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

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$\"\"$ .

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Differentiate $\"\"$ partially with respect to $\"\"$ .

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$\"\"$

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

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$\"\"$ .

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Step 3 :

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The equation of the tangent plane is $\"\"$ Substitute $\"\"$ , $\"\"$ and $\"\"$ in above equation. $\"\"$

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The equation of a tangent plane is $\"\"$ .

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Step 4 :

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(b)

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Find the equation of normal line :

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The equation of normal line is $\"\"$

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

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$\"\"$

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The equation of normal line is $\"\"$

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Solution :

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(a) The equation of a tangent plane is $\"\"$ .

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(b) The equation of normal line is $\"\"$