Formula for Normal Unit Vector on Ellipse at (x,y)

[GRDixon]

Given the formula for an ellipse in x and y and centered on the origin, I need a formula for the x and y components of the normal unit vector at any point (x,y) on the ellipse (y>0). My calculus skills are rusty, and I haven't been able to figure this out. Thanks in advance for any help.

 

[Gib Z]

Start with the equation of the ellipse. Differentiate implicitly to get the gradient of the tangent at (x,y) in terms of x and y. From that you can work out the gradient of the normal, and it's a simple application of trigonometry to separate for components.

 

[GRDixon]

Start with the equation of the ellipse. Differentiate implicitly to get the gradient of the tangent at (x,y) in terms of x and y. From that you can work out the gradient of the normal, and it's a simple application of trigonometry to separate for components.

Thanks, Gib. That's just the nudge I needed.