Could you check this question to see if I have done it right:

Question: Find the equation of the normal to the curve y=x+ 4/x at the point p where x=4. If the normal meets the curve agian at N, find the co-ordinates of N.

This is what I have done:

y= x+4x^-1

dy/dx= 1 - 4x^-2

x=4 y=(4)*4(4)^-1 = 5

dy/dx= 1 - 4(4)^-2 = 0.75 or 3/4

Normal gradient = -4/3

(y - 5) = -4/3(x - 4)

y - 5 = -4/3x + 16/3

y = -4/3x + 31/3 or 3y = - 4x + 31

This is where I got up to, i'm not to sure what you have to do when it says 'If the normal meets the curve agian at N, find the co-ordinates of N'

If you could please explain and check if I have done the first bit right.

Thank you