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  "body": "\n## Definition\n\nLet $Q$ be a non-degenerate conic section in the Euclidean plane $\\mathbb{R}^2$.\nSuppose that $Q$ is an [[ellipse|0VKCCEXBJ1]] or a [[hyperbola|0WN5G117YC]] with the foci $F_1$ and $F_2$, as in their definitions. Then $F_1$ and $F_2$ are the foci of $Q$. If $Q$ is a [[circle|060W5CBZP6]], its centre is its only focus.\nIf $Q$ is a [[parabola|04S2GMHX82]] with the focus $F$ and a directrix, as in its definition, then $F$ is the only focus of $Q$.\n\n## Remarks\n\nThe foci are determined by the conic. For the ellipse $\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$ with $a \u003e b \u003e 0$, the foci are $(\\pm c, 0)$ with $c^2 = a^2 - b^2$.\nFor the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$, the foci are $(\\pm c, 0)$ with $c^2 = a^2 + b^2$.\nLet $Q$ be a conic that is not a circle, and let $F$ be a focus of $Q$. Then $Q$ is the set of the points whose distances to $F$ and to a line, the [[directrix|0E5CXYNEPX]], have a constant ratio $e \u003e 0$.\n\n## Explanations\n\n### L1 human\n\nThe foci are the two pins in the string construction of an ellipse. A parabolic mirror sends the light of a lamp at its focus out in parallel rays. For the parabola $y = x^2/4$, the focus is $(0, 1)$.\n",
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        "locator": "Defining conics in terms of a focus and a directrix",
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