I'm currently working on the linear programming problem involving plotting level sets.
The first part of the problem asks me to plot the level sets of $z(x, y) = x^2 − y^2$
This wasn't too difficult for me, and the next part asks me to implicitly differentiate $x^2-y^2 = k$ and let $(x_0, y_0)$ be a point on this.
For this part I got $2yy' = 2x = dy/dx = x/y$
Part c) is where I'm a little lost. It says:
"Find an expression for a vector parallel to the tangent line at $(x_0, y_0)$ [Hint: you can use the slope you just found]"
Finding a parallel line wouldn't be to difficult as I'd just need to add a constant and keep the same slope, but I'm not exactly sure how I'd go about finding a parallel vector. As far as I know, the cross product is used to find a parallel line, but that would require 3 dimensions, right?
Any help would be greatly appreciated!