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  "body": "\n## Definition\n\nLet $Q$ be a non-degenerate [[conic section|00HJCMC2CD]] in the Euclidean plane $\\mathbb{R}^2$.\nIf $Q$ is a circle, its eccentricity is $e = 0$. Otherwise, let $F$ be a [[focus|0RBKKNH4GV]] of $Q$ and $\\ell$ the [[directrix|0E5CXYNEPX]] for $F$. The eccentricity of $Q$ is the constant ratio\n$$e = \\frac{d(P, F)}{d(P, \\ell)}, \\qquad P \\in Q.$$\n\n## Remarks\n\nAn ellipse has $0 \\leq e \u003c 1$, a parabola has $e = 1$ and a hyperbola has $e \u003e 1$.\nFor an ellipse or a hyperbola with the semi-major axis $a$ and the foci at the distance $c$ from the centre, $e = c / a$.\nTwo conic sections with the same eccentricity are similar.\n\n## Explanations\n\n### L1 human\n\nThe eccentricity tells how stretched a conic is. A circle has $e = 0$. The ellipse $\\frac{x^2}{25} + \\frac{y^2}{9} = 1$ has $c = 4$ and so $e = 4/5$. As $e$ gets near $1$, the ellipse becomes long and thin.\n",
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  "name": "Eccentricity",
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