Αποτελέσματα Αναζήτησης
16 Νοε 2022 · Quadric surfaces are the graphs of any equation that can be put into the general form \[A{x^2} + B{y^2} + C{z^2} + Dxy + Exz + Fyz + Gx + Hy + Iz + J = 0\] where \(A\), … , \(J\) are constants.
3 Αυγ 2023 · An elliptic cone is a cone with an elliptical cross-section. It has a directrix, which is an ellipse. Such a cone is different from the standard circular cone (with a circular cross-section) in shape. It is thus one of the quadric surfaces with traces composed of conic sections.
Quadric surfaces are the graphs of equations that can be expressed in the form A x 2 + B y 2 + C z 2 + D x y + E x z + F y z + G x + H y + J z + K = 0 . When a quadric surface intersects a coordinate plane, the trace is a conic section.
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 \( y=b\).
To repeat: We can slice through cones or we can look for equations. For a cone of light, we see an ellipse on the wall. (The wall cuts into the light cone.) For an equation AX^ + Bxy + Cy2+Dx + Ey + F = 0, we will work to make it simpler. The graph will be centered and rescaled (and rotated if necessary), aiming for an equation like y = x2 ...
An elliptical cone is a cone a directrix of which is an ellipse; it is defined up to isometry by its two angles at the vertex. Characterization: cone of degree two not decomposed into two planes. Contrary to appearances, every elliptical cone contains circles.
