how to extract y as a function of x

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Robert Jones
Robert Jones 2022-12-14
评论： Star Strider 2022-12-14
Hello,
I am trying to extract the y as a function of x in the expression below, using the symbolic toolbox.
Here is the the expression (the generalized formula of an offsetted, rotated ellipse).
(a^2*sin(tr)^2+b^2*cos(tr)^2)*(x-x0)^2+2*(b^2-a^2)*sin(tr)*cos(tr)*(x-x0)*(y-y0)+(a^2+cos(tr)^2+b^2*sin(tr))*(y-y0)^2==a^2*b^2;
I need to express y as a function of x. I undersand there might be more than one solutions.
I tried without success:
syms x y a b x0 y0 tr
fun=solve(y,x)
Apparently I do not know how to use the symbolic tollbox correctly
Help would be appreciated
Thank you

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采纳的回答

Star Strider
Star Strider 2022-12-14
Ran in:
Try something like this —
syms x y a b x0 y0 tr
sympref('AbbreviateOutput',false);
Eqn = (a^2*sin(tr)^2+b^2*cos(tr)^2)*(x-x0)^2+2*(b^2-a^2)*sin(tr)*cos(tr)*(x-x0)*(y-y0)+(a^2+cos(tr)^2+b^2*sin(tr))*(y-y0)^2==a^2*b^2;
Eqn = simplify(Eqn, 1000)
Eqn = 
fun = simplify(solve(Eqn,y),1000)
fun = 
Eqn = isolate(Eqn, y)
Eqn = 
.
  2 个评论
Robert Jones
Robert Jones 2022-12-14
移动：John D'Errico 2022-12-14
Great, Thank you. I will
Star Strider
Star Strider 2022-12-14
My pleasure!
If my Answer helped you solve your problem, please Accept it!
.

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