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| PAGE: 969 | SET: Exercises | PROBLEM: 43 |
The equation of a tangent plane :
The tangent plane equation at the point 
is
The normal line to the surface at the point 
is
(a)
The equation is 
and the point is 
.
Rewrite the equation as 
.
Consider 
.
Differentiate 
partially with respect to 
.
Substitute the point 
in above equation.
.
Differentiate 
partially with respect to 
.
Substitute the point 
in above equation.
.
Differentiate partially with respect to 
.
Substitute the point in above equation.
.
The equation of the tangent plane is 
Substitute 
, 
and 
in above equation. 
The equation of a tangent plane is 
.
(b)
Find the equation of normal line :
The equation of normal line is 
Substitute , and in above equation.
The equation of normal line is 
(a) The equation of a tangent plane is 
.
(b) The equation of normal line is 
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