SOLUTION: Determine the equation of the tangent plane to the sphere x^2 + y^2 + z^2 = 1 at the point (1/2, 1/2,{{{sqrt(2)/2}}}).

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Question 1045479: Determine the equation of the tangent plane to the sphere x^2 + y^2 + z^2 = 1 at the point (1/2, 1/2,sqrt%282%29%2F2).
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
The equation of the tangent plane to the surface 
%22F%28x%2Cy%2Cz%29%22%22%22=%22%220 at the point %28matrix%281%2C5%2Cx%5B0%5D%2C%22%2C%22%2Cy%5B0%5D%2C%22%2C%22%2Cz%5B0%5D%29%29%29

is

F%5Bx%5D%22%22%2B%22%22F%5By%5D%22%22%2B%22%22F%5Bz%5D %22%22=%22%22 0

x%5E2+%2B+y%5E2+%2B+z%5E2%22%22=%22%221
 
x%5E2+%2B+y%5E2+%2B+z%5E2-1%22%22=%22%220

%22F%28x%2Cy%2Cz%29%22%22%22=%22%22x%5E2+%2B+y%5E2+%2B+z%5E2-1

F%5Bx%5D%22%28x%2Cy%2Cz%29%22%22%22=%22%222x

F%5By%5D%22%28x%2Cy%2Cz%29%22%22%22=%22%222y

F%5Bz%5D%22%28x%2Cy%2Cz%29%22%22%22=%22%222z

F%5Bx%5D%28matrix%281%2C5%2C1%2F2%2C%22%2C%22%2C1%2F2%2C%22%2C%22%2Csqrt%282%29%2F2%29%29%29%22%22=%22%222%281%2F2%29%22%22=%22%221

F%5By%5D%28matrix%281%2C5%2C1%2F2%2C%22%2C%22%2C1%2F2%2C%22%2C%22%2Csqrt%282%29%2F2%29%29%29%22%22=%22%222%281%2F2%29%22%22=%22%221

F%5Bz%5D%28matrix%281%2C5%2C1%2F2%2C%22%2C%22%2C1%2F2%2C%22%2C%22%2Csqrt%282%29%2F2%29%29%29%22%22=%22%222%28sqrt%282%29%2F2%29%22%22=%22%22sqrt%282%29


So the equation of the tangent plane at %28matrix%281%2C5%2C1%2F2%2C%22%2C%22%2C1%2F2%2C%22%2C%22%2Csqrt%282%29%2F2%29%29%29 is

1%28x-1%2F2%29%2B1%28y-1%2F2%29%2Bsqrt%282%29%28z-sqrt%282%29%2F2%29%22%22=%22%220 

x-1%2F2%2By-1%2F2%2Bsqrt%282%29z-2%2F2%22%22=%22%220 

x-1%2F2%2By-1%2F2%2Bsqrt%282%29z-1%22%22=%22%220 

x%2By%2Bsqrt%282%29z-2%22%22=%22%220

Edwin