The ellipse is: $ x(t)=a \cos(wt-c)\\ y(t)=b \cos(wt-d) $
What are:
- major axis length
- minor axis length
- angle of major axis with $x$ axis?
- the parametric form ? $(ax^2+by^2+cxy+dx+fy+...=g)$
The ellipse is: $ x(t)=a \cos(wt-c)\\ y(t)=b \cos(wt-d) $
What are:
Expand $\cos(wt-c)$ and $\cos(wt-d)$ using $\cos(A-B)=\cos A\cos B+\sin A\sin B$
Solve for $\cos(wt), \sin(wt)$
Use $\cos^2(wt)+ \sin^2(wt)=1$ to remove $wt$ from the given equations to get
$x^2b^2+y^2a^2-2xyab\cos(c-d)-a^2b^2sin^2(c+d)=0$
Use Rotation of axes, to remove $xy$ term from the equation to get the standard form $\frac{X^2}{A^2}+\frac{Y^2}{B^2}=1$.
The major axis length= 2max$(A,B)$
The minor axis length= 2min$(A,B)$
The parametric form would be $(A\cos \alpha, B\sin \alpha)$