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Show that if the feet of the normals fro...

Show that if the feet of the normals from a point to the ellipse `x^2/a^2 + y^2/b^2 = 1` are coincident, the locus of the middle point of the chord joining the feet of the other two normals is `(xy/ab)^2 = (x^2/a^2 + y^2/b^2)^3`

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