Tanget of plane

[InfinLions]

Consider the surface given by z = 8 − 2x^2 - 2y^2 .
Determine a point on this surface at which the tangent plane is perpendicular to the line given by
x = 2 − 3t , y = 7 + 8t , z = 5 − t .
Hence, determine the equation of the tangent plane at this point

I looked up similar questions online but my solution for:
-6x = -3k
-4y = 8k
-1 = -1k
isn't the same for the values of k when comparing df and dt. (Assuming f(x,y,z) = 8 − 2x^ 2- 2y^2 - z

would appreciate any help

 

[Dr.Peterson]

Consider the surface given by z = 8 − 2x^2 - 2y^2 .
Determine a point on this surface at which the tangent plane is perpendicular to the line given by
x = 2 − 3t , y = 7 + 8t , z = 5 − t .
Hence, determine the equation of the tangent plane at this point

I looked up similar questions online but my solution for:
-6x = -3k
-4y = 8k
-1 = -1k
isn't the same for the values of k when comparing df and dt. (Assuming f(x,y,z) = 8 − 2x^ 2- 2y^2 - z

would appreciate any help

Please show the details of your work. Where did you get those three equations? Are you sure the first is what you intended? What was your solution? What did you compare it to?

 

[Eugenio]

[imath]\frac{\partial f}{\partial x}=-4x[/imath]. Am I wrong?

 

[Deleted member 4993]

[imath]\frac{\partial f}{\partial x}=-4x[/imath]. Am I wrong?

That is correct.

 

[Dr.Peterson]

[imath]\frac{\partial f}{\partial x}=-4x[/imath]. Am I wrong?

No, that's not wrong. Did you get -6x = -3k because of a wrong partial derivative?

Keep going and show the rest of your work, in detail.