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What Is the Z-Coordinate of the Point P(1,3,z)P ( 1,3 , z )

Question 99

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What is the z-coordinate of the point P(1,3,z)P ( 1,3 , z ) if P lies on the plane which is tangent to the ellipsoid 4x2+y2+9z2=174 x ^ { 2 } + y ^ { 2 } + 9 z ^ { 2 } = 17 at the point (1,2,1)( - 1 , - 2 , - 1 ) ? Give your answer to four decimal places.

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