how to extract y as a function of x

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

Answer 1

[Star Strider]

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 = 

.

[Robert Jones]

Great, Thank you. I will

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

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