Normal of a cone

This might be quite a simple question but I’m not sure how to do it,l and geometry isn’t my strong suite,
Say you have a cone defined by x^2 + z^2 - ( r -ry/h)^2

How would you find the normal to the surface of it? Given a point (x,y,z) which is on the side of the cone.

I thought it might be (x, r/h, z) normalised, if it was a cylinder it would just be (x,0,z) normalised but since it is a cone it will point upwards by theta, and theta should be tan^-1 r/h, so should the normal be ( x/r, r/h, z/r) or something??

Just a bit confused, thanks

Can you post the actual question? Im assuming that the equation fo the cone is = 0 and the equation corresponds to base (x,z) radius r (centered on the origin) and height h. To find the normal, you simply find the grad of f(x,y,z) and the unit normal will be simply normalized by the corresponding magnitude

Is their a way to do this without the use of vector fields? The specific module I am taking doesn’t assume this knowledge, and yea the equation is =0 and the base is the x z plane, with the apex on the y axis