(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1, where center is at (h,k), a is longer radius, and b is shorter radius {ellipse, conic}|. x = - h + a^2 / (a^2 + b^2)^0.5, where a > b.
foci
Ellipses have two focuses. Ellipse points have distances to foci. For all ellipse points, distance sum is constant.
Ellipses are symmetric about two lines. Ellipses have four points {vertex, ellipse} intersected by symmetry axes. Longest symmetry axis {major diameter} {major axis} has length = 2*a, where a > b. Shortest symmetry axis {minor diameter} {minor axis} has length = 2*b.
circle
Circle equation is (x - h)^2 + (y - k)^2 = r^2, where r is radius, and center is at (h,k).
auxiliary circle
A circle {auxiliary circle} with diameter equal major axis can surround ellipse.
Mathematical Sciences>Geometry>Solid>Cone>Conic Section>Sections
3-Geometry-Solid-Cone-Conic Section-Sections
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Date Modified: 2022.0224