Note that

So the function you are dealing with is a circle of radius

centered at

. This may be a helpful picture to have in your mind while doing this.

Given that

, the horizontal tangent occurs when the

*numerator* is zero (because then the derivative is 0), which is at

. Use the function to find that

.

Similarly, the vertical tangent occurs when the

*denominator* is zero (because then the derivative is "infinity"), which is at

. Use the function to find that

.

So the horizontal tangent lines occur at

and

and the vertical tangent lines occur at

and

.

If you think about the picture of the circle, this makes a lot of sense.