Locus problem

[RustyMind]

Locus of point such that tangents drawn from it to ellipse x²/a² + y²/b² = 1 intersect the coordinate axes at concyclic points


I found the combined equation of tangents but not sure what to do next ?

 

[Dr.Peterson]

I'm not sure what you mean by "combined equation of tangents". Can you show your work specifically, so we can be sure what you've done (and that it is right)?

Not having tried yet myself, I think I'd find the four intercepts, and write an equation that says they are concyclic. What might that equation look like? (What does concyclic mean, and how does it affect the lengths of such segments?)