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Analytic Geometry Parabola Ellipse Hyperbola Pdf Download

 
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MessagePosté le: Jeu 1 Sep - 08:00 (2016)    Sujet du message: Analytic Geometry Parabola Ellipse Hyperbola Pdf Download Répondre en citant




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Analytic Geometry Parabola Ellipse Hyperbola Pdf Download, cst tutorial for beginners pdf download

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Ellipse, Parabola, Hyperbola. How to create parabola. Parabola with axis parallel to $x$ axis. Length of major axis $A'A = 2a$ Length of minor axis $B'B = 2b$ Distance from center $C$ to focus $F$ or $F'$ is $c = sqrt{a^2 - b^2}$ Eccentricity = $epsilon = frac{c}{a} = frac{sqrt{a^2 - b^2}}{a}$ Equation in rectangular coordinates: $frac{(x - x0)^2}{a^2} + frac{(y - y0)^2}{b^2} = 1$ Equation in polar coordinates if $C$ is at $O$: $r^2 = frac{a^2b^2}{a^2 textrm{ sin }^2 theta + b^2 textrm{ cos }^2 theta}$ Equation in polar coordinates if $C$ is on $x$ axis and $F'$ is at $O$: $r = frac{a(1 - c^2)}{1 - c textrm{ cos } theta}$ If $P$ is any point on the ellipse, $PF + PF' = 2a$ If the major axis is parallel to the $y$ axis, interchange $x$ and $y$ in the above or replace $theta$ by $frac{1}{2}pi - theta$ [or $90^circ - theta$] . If parabola opens to left $(y - y0)^2 = -4a(x - x0)$ . If focus is at the origin the equation in polar coordinates is $r = frac{2a}{1 - textrm{ cos } theta}$ In case the axis is parallel to the $y$ axis, interchange $x$ and $y$ or replace $theta$ by $frac{1}{2}pi - theta$ [or $90^circ - theta$]. Length of major axis $A'A = 2a$ Length of minor axis $B'B = 2b$ Distance from center $C$ to focus $F$ or $F'$ is $c = sqrt{a^2 + b^2}$ Eccentricity = $epsilon = frac{c}{a} = frac{sqrt{a^2 + b^2}}{a}$ Equation in rectangular coordinates: $frac{(x - x0)^2}{a^2} - frac{(y - y0)^2}{b^2} = 1$ Slopes of asymptotes $G'H$ and $GH' = pm frac{b}{a}$ Equation in polar coordinates if $C$ is at $O$: $r^2 = frac{a^2b^2}{b^2 textrm{ cos }^2 theta - a^2 textrm{ sin }^2 theta}$ Equation in polar coordinates if $C$ is on $X$ axis and $F'$ is at $O$: $r = frac{a(c^2 - 1)}{1 - epsilon textrm{ cos } theta}$ If $P$ is any point on the hyperbola, $PF - PF' = pm 2a$ [depending on branch] If the major axis is parallel to the $y$ axis, interchange $x$ and $y$ in the above or replace $theta$ by $frac{1}{2}pi - theta$ [or $90^circ - theta$]. Hyperbola with center $C(x0 textrm{ , } y0)$ and major axis parallel to $x$ axis. If vertex is at $A(x0 textrm{ , } y0)$ and the distance from $A$ to focus$f$ is $a > 0$, the equation of the parabola is if parabola opens to right $(y - y0)^2 = 4a(x - x0)$ . How to create hyperbola..

Ellipse with center $C(x0 textrm{ , } y0)$ and major axis parallel to $x$ axis

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