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The point E is an arbitrary point on the parabola. The focus is F, the vertex is A (the origin), and the line FA is the axis of symmetry. The line EC is parallel to the axis of symmetry, intersects the x axis at D and intersects the directrix at C. The point B is the midpoint of the line segment FC.
A t-transitive graph is a graph such that the automorphism group acts transitively on t-arcs, but not on (t + 1)-arcs. Since 1-arcs are simply edges, every symmetric graph of degree 3 or more must be t-transitive for some t, and the value of t can be used to further classify symmetric graphs.
Graph of y = ax 2 + bx + c, where a and the discriminant b 2 − 4ac are positive, with. Roots and y-intercept in red; Vertex and axis of symmetry in blue; Focus and directrix in pink; Visualisation of the complex roots of y = ax 2 + bx + c: the parabola is rotated 180° about its vertex (orange).
Determine the symmetry of the curve. If the exponent of x is always even in the equation of the curve then the y-axis is an axis of symmetry for the curve. Similarly, if the exponent of y is always even in the equation of the curve then the x-axis is an axis of symmetry for the curve.
The axis of symmetry of a two-dimensional figure is a line such that, if a perpendicular is constructed, any two points lying on the perpendicular at equal distances from the axis of symmetry are identical. Another way to think about it is that if the shape were to be folded in half over the axis, the two halves would be identical as mirror ...
Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object
The smallest asymmetric regular graphs have ten vertices; there exist 10-vertex asymmetric graphs that are 4-regular and 5-regular. [2] [3] One of the five smallest asymmetric cubic graphs [4] is the twelve-vertex Frucht graph discovered in 1939. [5] According to a strengthened version of Frucht's theorem, there are infinitely many asymmetric ...
Since both the transverse axis and the conjugate axis are axes of symmetry, the symmetry group of a hyperbola is the Klein four-group. The rectangular hyperbolas xy = constant admit group actions by squeeze mappings which have the hyperbolas as invariant sets.