# How to find the straight tangent line?

• Helloooo

#### Helloooo

Homework Statement
Find the straight tangent line at (2,-1) to the level curve of f(x,y)=x^2-y^2
Relevant Equations
f(x,y)=x^2-y^2
Point: (2,-1)

and have the tangent plane:

4x+2y+3=0

3=2x+y

And i really don´t understand why.

and have the tangent plane:

4x+2y+3=0
No you don’t. Inserting (2,-1) in the LHS gives 4*2+2(-1) = 8-2 = 6 so the required point is not on that plane.

No you don’t. Inserting (2,-1) in the LHS gives 4*2+2(-1) = 8-2 = 6 so the required point is not on that plane.
Firstly i noticed an error in my writing.
The tangent plane i got was 4x+2y-3=0.
I´m sorry for that
So i redid the tangent plane to
4x+2y-6=0
However i still don´t know how to fint the straight tangent line.
Thank you

However i still don´t know how to fint the straight tangent line.
That's it, right there:
4x+2y-6=0

That's it, right there:
Does that mean that the tangent plane and straight tangent line is the same?
If so, why are they called differently or is it just in this particulary problem?

Does that mean that the tangent plane and straight tangent line is the same?
If so, why are they called differently or is it just in this particulary problem?
In two dimensions, a tangent line and the tangent plane are the same thing. In n dimensions the tangent plane has n-1 dimensions. It is a more general concept because it is not restricted to two dimensions.

Lnewqban
In two dimensions, a tangent line and the tangent plane are the same thing. In n dimensions the tangent plane has n-1 dimensions. It is a more general concept because it is not restricted to two dimensions.
I see, thank you so much for your help!