## Partial Derivative

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

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

So the parametric equations of L are:
$$x=1$$
$$y=2+t$$
$$z=4-4t$$

Am I doing this correct? Thanks.

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