Angle between two curves

[FRANCESCO]

In the problem of finding the angle between the curves x^2+y^2=5 and x^2-y^2=3 at (2,1), when I calculate the dot product of normal vectors df/dx i+ df/dy j, I get the correct answer of arcos (3/5).
But as the curve f(x,y) =c has slope -df/dy/df/dy, the tangent vectors can be written df/dy i –df/dx j right?
If I calculate dot product between the two tangent vectors I get 0.
What’s wrong in the reasoning?
Thanks in advance to all those who’ll find the time to help

 

[Deleted member 4993]

In the problem of finding the angle between the curves x^2+y^2=5 and x^2-y^2=3 at (2,1), when I calculate the dot product of normal vectors df/dx i+ df/dy j, I get the correct answer of arcos (3/5).
But as the curve f(x,y) =c has slope -df/dy/df/dy, the tangent vectors can be written df/dy i –df/dx j right?
If I calculate dot product between the two tangent vectors I get 0.
What’s wrong in the reasoning?
Thanks in advance to all those who’ll find the time to help

What is that?

Other than silly mistakes like that - your reasoning is correct.

So show your complete work - may be we can find the mistake!