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  "body": "\n## Summary\n\nA quadric is the set of points of an affine or projective space where a polynomial of degree $2$ vanishes.\nConics in the plane and quadric surfaces such as spheres, ellipsoids and hyperboloids in space are quadrics.\nIn projective geometry, a quadric is given by a [[quadratic form|0RBQS1JJCR]].\nThe points, lines and subspaces lying on a non-degenerate quadric form a [[polar space|Z7T0V2VAWJ]].\n\n## Explanations\n\n### L1 human\n\nA quadric is the next simplest shape after a flat one: flat sets are cut out by equations of degree $1$, quadrics by equations of degree $2$.\nThe sphere $x^2 + y^2 + z^2 = 1$ is a quadric in space.\nSo is the saddle $z = xy$, which contains two families of straight lines.\nIn the projective setting all equations are written homogeneously, for example $x_0 x_1 + x_2 x_3 = 0$.\n",
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