Line Tangent to following surface

[mopar969]

What is the solution to:
What is the equation of a line tangent to the following surface z=6-(4x^2)-(y^2) at the point (5,3,-103)

 

[tiny-tim]

hi mopar969!

show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[HallsofIvy]

You ask for the equation of a line tangent to a surface. There will be a whole plane tangent to the surface and any line lying in that plane will be tangent to the surface. Do you know how to find the tangent plane to a surface?

 

[mopar969]

I thought that maybe I need to find the normal vector first to start this problem but I am not sure please help.

 

[tiny-tim]

that would certainly do it!

 

[HallsofIvy]

If a surface is described by f(x,y,z)= constant, then \nabla f is perpendicular to the surface.

 

[WatermelonPig]

Let z = f(x,y). z is "three-dimensional" so its tangent must be "two-dimensional".

T: z -z0 = . . . you finish the rest.