Given a function $f(x,y)$ how to get the points where the tangent has a certain given slope?

39 Views Asked by At

For example let the the function given be $f(x,y)=x^2+y^2$ slope given be 2.
My first intuition would be getting the gradient of the function which would be $2i+2j$ then setting it equal to the given slope and solving such that: $2i+2j=2$
Then this looked to me that I am considering the gradient the same as the tangent which is wrong as they are perpendicular
What am I doing wrong?