Please tell me the definition of this problem

[rado5]

Homework Statement

Find the unique vector which is perpendicular on x²+y²=100 at (x₀,y₀)=(6,8).

Homework Equations

$$\nabla$$F$$/$$ $$\left|$$ $$\nabla$$F $$\left|$$

The Attempt at a Solution

I think the solution is $$\nabla$$F$$/$$ $$\left|$$ $$\nabla$$F $$\left|$$ but I don't know how to calculate $$\nabla$$F for x²+y²=100
I know $$\nabla$$F=($$\partial$$F$$/$$$$\partial$$x,$$\partial$$F$$/$$$$\partial$$y,$$\partial$$F$$/$$$$\partial$$z)
Please tell me how I can find the answer. What is F here?

 

[Dick]

F(x,y)=x^2+y^2-100. The level surface is F(x,y)=0. Now do the gradient. Or F(x,y)=x^2+y^2 and the level surface is F(x,y)=100, your choice.

 

[rado5]

So in this case the solution is $$\nabla$$F$$/$$$$\left|$$$$\nabla$$F$$\left|$$ = (0.6,0.8) Is it correct?
($$\nabla$$F=(2x,2y)).

 

[Dick]

So in this case the solution is $$\nabla$$F$$/$$$$\left|$$$$\nabla$$F$$\left|$$ = (0.6,0.8) Is it correct?
($$\nabla$$F=(2x,2y)).

If you mean to find the unit normal to the circle, sure, that's right.

 

[rado5]

Thank you very much really. I actually translated the problem from persian to English, but I think it is now correct. Again thank you very much for your great generosity.