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hyperbola

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hyperbola
hyperbola Geom. (haɪˈpɜːbələ) [a. mod.L. hyperbola, ad. Gr. ὑπερβολή the name of the curve, lit. excess (cf. hyperbole), f. ὑπερβάλλειν to exceed (ὑπέρ over + βάλλειν to throw). In F. hyperbole. The hyperbola was so named either because the inclination of its plane to the base of the cone exceeds th... Oxford English Dictionary
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Feuerbach hyperbola
The line is tangent to this hyperbola at . The pedal circle of any point on the hyperbola passes through the Feuerbach point, the center of the hyperbola. wikipedia.org
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hyperbola
hyperbola/haɪˈpɜ:bələ; haɪ`pəbələ/ n(geometry 几) curve produced when a cone is cut by a plane that makes a larger angle with the base than the side of the cone makes 双曲线. =>illus 见插图. 牛津英汉双解词典
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Unit hyperbola
When the conjugate of the unit hyperbola is in use, the alternative radial length is The unit hyperbola is a special case of the rectangular hyperbola on the unit hyperbola. wikipedia.org
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Hyperbolas - Standard Form This is probably a simple question but if $y = \frac{1}{x}$ is a hyperbola, then how does it comply with the standard form of a hyperbola? !Standard Form of Hyperbola
In general, for any angle of rotation $\theta$ from the $x-$axis, we may apply the following change of variable to put a hyperbola in standard form: $ $x = x\cos\theta - y'\sin\theta$$ $$y = x'\sin\theta +y'\cos\theta.$$ Notice our hyperbola $xy = 1$ is rotated by an angle of $\frac{\pi}{4}$ from the
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Hesperorhipis hyperbola
Hesperorhipis hyperbola is a species of metallic wood-boring beetles in the family Buprestidae. It is found in North America. Subspecies H. hyperbola californica Knull, 1947 H. hyperbola hyperbola Knull, 1938 References "A catalog and bibliography of the Buprestoidea of America wikipedia.org
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Quick question about a hyperbola in $\log-\log$ space Let $u=\ln(x)$ and $v=\ln(y).$ Is it correct to conclude that $uv=1,$ in $\log-\log,$ space is a hyperbola, but in $x,y$ space it is not a hyperbola?
It is indeed correct to conclude that in log-log space $\ln(x)\ln(y)=1$ is the hyperbola $xy=1.$ Taking the natural logarithm of each point of the plot
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Dirichlet hyperbola method
In number theory, the Dirichlet hyperbola method is a technique to evaluate the sum where are multiplicative functions with , where is the Dirichlet Since , the Dirichlet hyperbola method gives us the result Wherer is the Euler–Mascheroni constant. wikipedia.org
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Equation of hyperbola from asymptote? > A line $y = 2x+5$ intersects a hyperbola only at a point $(-2,1)$. The equation of one of its asymptotes is $3x+2y+1=0$. If hyperbola passes through the point $(-1,0)$ then what...
As line $y=2x+5$ intersects the hyperbola only at a single point (but it is not tangent), then this line must be parallel to an asymptote. On the other hand, if $2x−y+λ=0$ and $3x+2y+1=0$ are the equations of its asymptotes, then the equation of the hyperbola is $$ (2x−y+λ)(3x+2y+1)=k, $$
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Meaning of Hyperbola in Chinese is : 双曲线 - StudySite.org
Hyperbola: Chinese Meaning: 双曲线 an open curve formed by a plane that cuts the base of a right circular cone / A curve formed by a section of a cone, when the cutting plane makes a greater angle with the base than the side of the cone makes.
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Equation representing the branch of hyperbola Is there an equation representing the one branch of hyperbola ($x^2-y^2=1$). This is the regular hyperbola: ![enter image description here]( This is the expected curve:...
In order to "exclude" possible negative $x$ we can do the trick of taking the square root, since this is not possible for negative numbers, then cancel the square root by using a square. Thus the equation will be identical as the one above, but only defined on the positive numbers for $x$. $$(\sqrt ...
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Hyperbola GNU/Linux-libre
Hyperbola GNU/Linux-libre被自由软件基金会列在完全自由的作业系统中，符合他们的GNU自由系统散布版指南。 历史 Hyperbola诞生于第十七届的国际自由软体论坛（于巴西阿雷格里港举办）。 2018年12月6日，Hyperbola成了第一个被GNU认可为完全自由专案的巴西散布版，让它变成了自由软体基金会自由散布版清单的一部份。 社会契约 Hyperbola建立了一份社会契约。 wikipedia.org
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OpenCASCADE Conic to BSpline Curves-Hyperbola - eryar - C++博客
OpenCASCADE Conic to BSpline Curves-Hyperbola. eryar@163.com. Abstract. Rational Bezier Curve can represent conic curves such as circle, ellipse, hyperbola, .etc. www.cppblog.com
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Equation of a hyperbola given its asymptotes > Find the equation of the hyperbola whose asymptotes are $3x-4y+7$ and $4x+3y+1=0$ and which pass through the origin. The equation of the hyperbola is obtained in my refe...
$$ \frac{4x+3y+1}{5}=\pm\frac{3x-4y+7}{5}\\\ \implies x+7y-6=0\;;\; 7x-y+8=0\text{ which are the axis of the hyperbola with centre }(-1,1)\\\ $$ Since $m_1m_2=-1\implies$ asymptotes are perpendicular $\implies$ rectangular hyperbola $$ \frac{(x+7y-6)^2}{50a^2}-\frac{(7x-y+8)^2}{50a^2}=\pm1\\\ \text{At
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Is the graph of $y=\frac{k}{x}$ a hyperbola? Is the graph of the following inverse relation a hyperbola?$$y=\frac kx$$ If yes, is it the only kind of hyperbola whose equation is an explicit function?
Yes, $$y=\frac kx$$ is a hyperbola. In fact, it is a type of _rectangular hyperbola_ which you can read more about here. This means that a function $y(x)$ that takes the form $$y-k=\frac {k}{x-h}$$ is also hyperbola.
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