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[标准] 二次曲线内点-point lie within the quadric curve

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发表于 2017-5-29 22:55:04 | 显示全部楼层 |阅读模式 | 百度 
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x
输入的解释:
quadratic curves
名为曲线:
circle | circle parallel curve | circular arc | ellipse | hyperbola | parabola | parabolic segment | rectangular hyperbola | semicircle (total: 9)
例图:
循环:
圆平行曲线:
圆弧:
备选的名字:
等轴双曲线:
equilateral hyperbola | right hyperbola
半圆:
half-circle
方程:
参数方程:
circle | x(t) = a cos(t)y(t) = a sin(t)circle parallel curve | x(t) = (a + k) cos(t)y(t) = (a + k) sin(t)circular arc | x(t) = a cos(t)y(t) = a sin(t)ellipse | x(t) = a cos(t)y(t) = b sin(t)hyperbola | x(t) = a sec(t)y(t) = b tan(t)parabola | x(t) = 2 a ty(t) = a t^2parabolic segment | x(t) = ty(t) = h (1 - t^2/a^2)rectangular hyperbola | x(t) = a sec(t)y(t) = a tan(t)semicircle | x(t) = a cos(t)y(t) = a sin(t)
Semialgebraic描述:
circular arc | x^2 + y^2 = a^2 and -p/2<=tan^(-1)(x, y)<=p/2parabolic segment | a^2 (y - h) + h x^2 = 0 and y>0semicircle | x^2 + y^2 = a^2 and y>=0
笛卡儿方程:
circle | x^2 + y^2 = a^2circle parallel curve | x^2 + y^2 = (a + k)^2ellipse | x^2/a^2 + y^2/b^2 = 1hyperbola | x^2/a^2 - y^2/b^2 = 1parabola | y = x^2/(4 a)rectangular hyperbola | x^2 - y^2 = a^2
极坐标方程:
circle | r(θ) = acircle parallel curve | r(θ) = a + kcircular arc | r(θ) = aellipse | r(θ) = (a b)/sqrt((b^2 - a^2) cos^2(θ) + a^2)hyperbola | r(θ) = (a b)/sqrt(b^2 cos^2(θ) - a^2 sin^2(θ))parabola | r(θ) = 4 a tan(θ) sec(θ)rectangular hyperbola | r(θ) = a sqrt(sec(2 θ))semicircle | r(θ) = a
共同的属性:
algebraic | parametric | quadratic
基本属性:
半径:
circle | r = acircular arc | r = a
弦长:
circular arc | 2 a sin(p/2)
直径:
circle | d = 2 a
围:
circle | C = 2 π a
封闭的领域:
circle | A = π a^2circle parallel curve | A = π (a + k)^2ellipse | A = π a bparabolic segment | A = (4 a h)/3semicircle | A = (π a^2)/2
电弧长度:
circle | s = 2 π acircle parallel curve | s = 2 π (a + k)circular arc | s = a pellipse | s = 4 a E(1 - b^2/a^2)parabolic segment | s = sqrt(a^2 + 4 h^2) + (a^2 sinh^(-1)((2 h)/a))/(2 h)semicircle | s = π a
代数学位:
circle | d = 2circle parallel curve | d = 2circular arc | d = 2ellipse | d = 2hyperbola | d = 2parabola | d = 2parabolic segment | d = 2rectangular hyperbola | d = 2semicircle | d = 2
二次曲线的性质:
 | eccentricity | focal parameter | semilatus rectumcircle | e = 0 | | circle parallel curve | e = 0 | | ellipse | e = sqrt(1 - b^2/a^2) | p = b^2/sqrt(a^2 - b^2) | L = b^2/ahyperbola | e = sqrt(b^2/a^2 + 1) | p = b^2/sqrt(a^2 + b^2) | parabola | e = 1 | p = 2 a | L = 2 arectangular hyperbola | e = sqrt(2) | p = a/sqrt(2) |  | foci | asymptotes | directrixellipse | {(-sqrt(a^2 - b^2), 0), (sqrt(a^2 - b^2), 0)} | | piecewise | {x = -a^2/sqrt(a^2 - b^2) ∨ x = a^2/sqrt(a^2 - b^2)} | b<a{y = -b^2/sqrt(b^2 - a^2) ∨ y = b^2/sqrt(b^2 - a^2)} | b>a | (otherwise)hyperbola | {(-sqrt(a^2 + b^2), 0), (sqrt(a^2 + b^2), 0)} | y = -(b x)/a ∨ y = (b x)/a | x = -a^2/sqrt(a^2 + b^2) ∨ x = a^2/sqrt(a^2 + b^2)parabola | {(0, a)} | | y = -arectangular hyperbola | {(-sqrt(2) a, 0), (sqrt(2) a, 0)} | | x = -a/sqrt(2) ∨ x = a/sqrt(2)
派生的曲线:
 | evolute | involutecircle | point at origin | circle involutecircle parallel curve | point at origin | ellipse | ellipse evolute | ellipse involuteparabola | semicubical parabola | parabola involutesemicircle | point at origin |
距离属性:
 | mean line segment lengthcircle | s^_ = (4 a)/πcircle parallel curve | s^_ = (4 (a + k))/πsemicircle | s^_ = (8 (π - 2) a)/π^2
相关单位:
 | filled region | related Wolfram Language symbolscircle | disk | Circlecircular arc | circular sector | Circleellipse | ellipse | Circle | associated peoplecircle | Ahmes | Thales | Euclid | Anaxagoras | Apollonius of Pergaellipse | Menaechmus | Euclid | Apollonius of Perga | Pappus | Johannes Kepler | Edmond Halley | Srinivasa Aiyangar Ramanujanhyperbola | Menaechmus | Euclid | Aristaeus the Elder | Apollonius of Perga | Pappusparabola | Menaechmus | Euclid | Apollonius of Perga | Pappus | Blaise Pascal | Galileo Galilei | David Gregory | Isaac Newton


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