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

Essay

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