An Interesting Locus

The standard cartesian ellipse x2a2+y2b2=1 \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 where a>ba>b has the director circle x2+y2=a2+b2x^2+y^2=a^2+b^2. The director circle, by definition, produces two tangents from any point on it that are perpendicular to each other. Now, at the points of contact, produce normals and let their point of intersection be LL. Let Z be the locus of all points L such that everything described as above is true. My question is simple, but messy. What is the algebraic relation that describes ZZ, for any value of aa and bb?

Note by Jack Lam
3 years, 10 months ago

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