The radical axis is defined as the locus of points for which the power of the point (the difference of the squares of the distances from the point to the centers of the two circles) is equal

In other words, for any point P on the radical axis, the equation (C₁P)² - (C₂P)² = 0 holds true.

This is the wrong definition, it defines the perpendicular bisector between the two centers, not the power bisector. In fact you can see that the radius is out of the equation inside this definition.

    assertAlmostEqual(radicalAxis({x: 3, y: 2, r: 5}, {x: 8, y: 7, r: 4}), {a: -0.7071067811865475, b: -0.7071067811865475, c: 7.707463914933368});

Is this even correct? The midpoint 5.5, 4.5 is clearly inside the radical axis, but 5.5*a + 4.5+b + c is around 0.636396, not 0.

Return an object with the properties a, b, and c representing the coefficients of the radical axis equation in the form ax + by + c = 0.

The description forgot to mention that a^2 + b^2 = 1 and c >= 0. Without this there are infinitely many solutions of (a, b, c).

Edit: Actually c >= 0 is not the correct criteria, in random tests the sign sometimes differ. Anyways because of this both (a, b, c) and (-a, -b, -c) are valid solutions.

Maybe I misunderstood something but...

be externally tangent, or not intersect at all, but they are never the same or internally tangent.

Aren't those two cases totally equivalent, considering the output? (superposed points). And that kind of output still isn't described (there is no line => ??)

Thanks again for adressing the issues, I've tried to solve them all. Let me know if you find anything else that needs to be fixed.

Thanks for the comment, I'll try to fix all the issues you mentioned.

Hi,

• The coefficient shouldn't be rounded. You should instead use custom assertions allowing for a margin on each value.

• the following outcomes aren't talked about:

  • what if there is one point only?
  • what if the circles do not intersect?

  If those cases never occur, it should be said in the description.

Cheers

Honestly i figured I know what you mean, I've removed my explaination for it. I guess you can figure it out on your own.

I thought giving advice wasnt generally a bad idea, what do you think should I remove from my description?

What was the point of telling the user what code to write?

Should be fixed now.

OH, yes of course. My bad.

How and why does this work? Could you show me how to fix this?

foo

what the?