No. and the fact that you have in your answer makes this obvious. the only variables should be x and y.

. When , , so the point the normal line passes through is (8,4). Now we need to find the slope.

Differentiating implicitly we see that . Which means the slope when y = 4 is 1/4. which implies the slope of the normal line is -4.

I think you can take it from here.

(did you make an error? should this be in precalc or calc?)