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[Paragon]

For a big circle $C$ centered at $(0,0)$, the locus of points that the sum of distances to Y-axis and to $C$ is $1$, is a parabola. What is the locus if we replace $C$ by a big ellipse

$\left(\,\right. \frac{x}{a}\left.\,\right)^2+\left(\,\right. \frac{y}{b}\left.\,\right)^2 = 1 ?$