Examples of using Hyperbola in English and their translations into Russian
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In Minkowski's development the hyperbola of type(B) above is in use.
A hyperbola meets it at two real points corresponding to the two directions of the asymptotes.
For determining the division value on the scale t', the hyperbola t2-x2 =1 should be used.
Given a hyperbola with asymptote A, its reflection in A produces the conjugate hyperbola. .
So the cissoid of two non-parallel lines is a hyperbola containing the pole.
Previous article Insert a hyperbola through the input field and change the constant a by slider.
At most populated latitudes andat most times of the year, this conic section is a hyperbola.
Assume there is some lattice point(x, y) on some hyperbola and without loss of generality x< y.
A hyperbola is uniquely determined by its foci F 1, F 2{\displaystyle F_{ 1},\;F_{2}} and a point not on the axes of symmetry.
Keywords: algebra, geometry, Mathcad,parabola, hyperbola, ellipse, Cassini oval, Apollonian circle, pokemon.
Then whichever hyperbola(A) or(B) is used, the operation is an example of a hyperbolic involution where the asymptote is invariant.
Specifically: It is the inverse with respect to the unit circle of the hyperbola 2 x a( 3 x 2- y 2){\displaystyle 2x=a3x^{2}-y^{2.
The higher the price, the lower is the demand or the higher the supply at one time or another,so the price curve looks like a hyperbola.
When e> 1 the original curve is a hyperbola and the inverse forms two loops with a crunode at the origin.
The same process of finding smaller roots is used instead to find lower lattice points on a hyperbola while remaining in the first quadrant.
In the mixture of confocal ellipses andhyperbolas, any ellipse intersects any hyperbola orthogonally at right angles.
To get rid of it you need to subtract the surface of the first or the second order(plane,parabola, or hyperbola) from the initial value matrix.
A similar derivation show that, conversely, any hyperbola is the cissoid of two non-parallel lines relative to any point on it.
For example, one or two foci can be used in defining conic sections, the four types of which are the circle, ellipse,parabola, and hyperbola.
Along the hyperbola x y 1{\displaystyle xy=1}, the Tutte polynomial of a planar graph specialises to the Jones polynomial of an associated alternating knot.
This line meets the circumcircle of ΔABC in 0,1, or 2 points according as the circumconic is an ellipse,parabola, or hyperbola.
Because a point of the hyperbola determines the parameter a{\displaystyle a} uniquely, any two hyperbolas of the pencil have no points in common.
If the problem is restricted to the class of planar graphs, the points on the hyperbola H 2{\displaystyle H_{2}} become polynomial-time computable as well.
Friedrich Wilhelm August Ludwig Kiepert(6 October 1846- 5 September 1934)was a German mathematician who introduced the Kiepert hyperbola.
P=920-en In GeoGebra can also“insert” a hyperbola via input field, and use a sliders til at ændre på konstanten a i forskriften for hyperblen.
Thus, for k=2, D(x) D2(x) counts the number of points on a square lattice bounded on the left by the vertical-axis,on the bottom by the horizontal-axis, and to the upper-right by the hyperbola jk x.
A hyperbola can be defined as the locus of points for each of which the absolute value of the difference between the distances to two given foci is a constant.
When a b the ellipse is a circle andthe conjugate diameters are perpendicular while the hyperbola is rectangular and the conjugate diameters are hyperbolic-orthogonal.
In context of the two-body problem in general relativity, trajectories of objects with enough energy to escapethe gravitational pull of the other, no longer are shaped like an hyperbola.
A, each magenta hyperbola connects all events having some fixed spacelike separation from the origin, while the green hyperbolae connect events of equal timelike separation.