Locus of tangent points to a family of confocal conics

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We take the family of ellipses with foci (a,0), (-a, 0) whose generic member we pass through the point (0,t). We look at the locus of the points of intersection of the tangent through the point (b,0).

The locus is clearly a circle. What is its center and radius?

Expressions

Name Input
Point G Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Locus Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image