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User:5849206328x: Difference between revisions

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//real f(real x) { return 3 * (-1/x + 1/(2*x^2)); }
//real f(real x) { return 3 * (-1/x + 1/(2*x^2)); }
//pair g(real t, real k) { return (1/k * 3/5 * (1 - e^(-k * t)), -t/k + 1/k * (4/5 + 1/k) * (1 - e^(-k * t))); }
pair g(real t) { return 16/(1 + 5/3 * cos(pi * t/180)) * dir(t); }


//draw(graph(f,0.0001,5));
draw(graph(g,-105,105));


pair A = (7, 4 * sqrt(141)/5);
pair A = (4, 8 * sqrt(10)/3);


draw(ellipse((-15,0),25,20)); draw((-50,0)--(20,0)); draw((-15,-25)--(-15,25)); draw((0,0)--(0,16),dashed);
draw((-25,0)--(25,0)); draw((15,-25)--(15,25)); draw((0,0)--(0,16),dashed);
dot((0,0)); draw((0,0)--A--(A + (-3,4.1)),EndArrow); dot(A);  
dot((0,0)); draw((0,0)--A--(A + (-1.7,4.1)),EndArrow); dot(A);
draw((-15,-40)--(30,20),dashed); draw((-15,40)--(30,-20),dashed);


label("$O$",(0,0),S); label("$ea$",(-8,0),S); label("$a$",(-28,0),S); label("$b$",(-15,10),W); label("$l$",(0,8),W);
//label("$O$",(0,0),S); label("$ea$",(-8,0),S); label("$a$",(-28,0),S); label("$b$",(-15,10),W); label("$l$",(0,8),W);
label("$\mathbf{r}$",A/2,NW); label("$\theta$",(1,0),NE); label("$m$",A,NE);
//label("$\mathbf{r}$",A/2,NW); label("$\theta$",(1,0),NE); label("$m$",A,NE);


//limits((-1,-2),(5.2,3.2),Crop);
limits((-25,-25),(25,25),Crop);


// e = 3/5, l = 9, a = 25, b = 20
// e = 5/3, l = 16, a = 9, b = 12
// (x + 15)^2/25^5 + y^2/20^2 = 141 * 400/625 = 141 * 16/25
// (x - 15)^2/81 - y^2/144 = 1, y^2/144 = 40/81, 40 * 144/81, sqrt(40) * 12/9 = 8sqrt(10)/3
</asy>
</asy>

Revision as of 20:03, 19 July 2015

[asy] import slopefield; //size(288); real e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353; real pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286; // Label f; // f.p=fontsize(6); //xaxis(0,5); //yaxis(-2,3); //real f(real x) { return 3 * (-1/x + 1/(2*x^2)); } pair g(real t) { return 16/(1 + 5/3 * cos(pi * t/180)) * dir(t); } draw(graph(g,-105,105)); pair A = (4, 8 * sqrt(10)/3); draw((-25,0)--(25,0)); draw((15,-25)--(15,25)); draw((0,0)--(0,16),dashed); dot((0,0)); draw((0,0)--A--(A + (-1.7,4.1)),EndArrow); dot(A); draw((-15,-40)--(30,20),dashed); draw((-15,40)--(30,-20),dashed); //label("$O$",(0,0),S); label("$ea$",(-8,0),S); label("$a$",(-28,0),S); label("$b$",(-15,10),W); label("$l$",(0,8),W); //label("$\mathbf{r}$",A/2,NW); label("$\theta$",(1,0),NE); label("$m$",A,NE); limits((-25,-25),(25,25),Crop); // e = 5/3, l = 16, a = 9, b = 12 // (x - 15)^2/81 - y^2/144 = 1, y^2/144 = 40/81, 40 * 144/81, sqrt(40) * 12/9 = 8sqrt(10)/3 [/asy]

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