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5 ημέρες πριν · The parametric equations for an elliptic cone of height h, semimajor axis a, and semiminor axis b are x = a (h-u)/hcosv (1) y = b (h-u)/hsinv (2) z = u, (3) where v in [0,2pi) and u in [0,h]. The elliptic cone is a quadratic ruled surface, and has volume V=1/3piabh.
11 Σεπ 2024 · The trace in plane \( z=5\) is the graph of equation \( x^2+\dfrac{y^2}{2^2}=1\), which is an ellipse. In the \(xz\)-plane, the equation becomes \( z=5x^2\). The trace is a parabola in this plane and in any plane with the equation \( y=b\).
16 Νοε 2022 · In the case of a cone the variable that sits by itself on one side of the equal sign will determine the axis that the cone opens up along. For instance, a cone that opens up along the \(x\)-axis will have the equation, \[\frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} = \frac{{{x^2}}}{{{a^2}}}\]
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Elliptic cone. Other name: degree-two cone (implying: non-decomposed). Reduced equation: (with , cone of revolution if and only if a = b). Sections by the plane z = k are ellipses with half-axes ak/h and bk/h. Developable ruled quadric. Cartesian parametrization: .
10 Ιαν 2011 · This video explains how to determine the traces of an elliptical cone and how to graph an elliptical cone.http://mathispower4u.yolasite.com/.
