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Print/export Download as PDF; Printable version; In other projects ... A parabola is a specific type of function. Relative to set theory
In the theory of quadratic forms, the parabola is the graph of the quadratic form x 2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x 2 + y 2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x 2 − y 2. Generalizations to more variables yield ...
Print/export Download as PDF; Printable version; In other projects ... Parabola; Hyperbola. Unit hyperbola; Degree 3. Cubic plane curves include
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The conic sections – circles, ellipses, parabolas, and hyperbolas – are plane sections of a cone with the cutting planes at various different angles, as seen in the diagram at left. Any cross-section passing through the center of an ellipsoid forms an elliptic region, while the corresponding plane sections are ellipses on its surface.
While a parabolic arch may resemble a catenary arch, a parabola is a quadratic function while a catenary is the hyperbolic cosine, cosh(x), a sum of two exponential functions. One parabola is f(x) = x 2 + 3x − 1, and hyperbolic cosine is cosh(x) = e x + e −x / 2 . The curves are unrelated.
A parabolic segment is the region bounded by a parabola and line. To find the area of a parabolic segment, Archimedes considers a certain inscribed triangle. The base of this triangle is the given chord of the parabola, and the third vertex is the point on the parabola such that the tangent to the parabola at that point is parallel to the chord.
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