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    • https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Celestial_Mechanics_(Tatum)/04%3A_Coordinate_Geometry_in_Three_Dimensions/4.04%3A_The_Paraboloid
      Here \(a\) and \(h\) are distances such that \(x = a\) when \(z = h\), and the length of the semi latus rectum is \(l = a^2 /(2h)\). The section in the plane \(y = 0\) is the "nose down" parabola \(x^...Here \(a\) and \(h\) are distances such that \(x = a\) when \(z = h\), and the length of the semi latus rectum is \(l = a^2 /(2h)\). The section in the plane \(y = 0\) is the "nose down" parabola \(x^2 = a^2 z / h\) extending above the xy-plane. The section in the plane \(x = 0\) is the "nose up" parabola \(y^2 = -b^2 z /h \) extending below the \(xy\)-plane.

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