Partial Derivative

Stevecgz

Question: Let C be the trace of the paraboloid [tex]z=9-x^2-y^2[/tex] on the plane [tex]x=1[/tex]. Find parametric equations of the tangent line L to C at the point P(1,2,4).

What I did:
[tex]z=8-y^2, x=1[/tex]
[tex]f_{y}=-2y[/tex]
[tex]f_{y}(1,2)=-4[/tex]

So the parametric equations of L are:
[tex]
x=1
[/tex]
[tex]
y=2+t
[/tex]
[tex]
z=4-4t
[/tex]

Am I doing this correct? Thanks.