A curve has parametric equations
$x=a \sin(t)+b \cos(t)$
$y=a \cos(t)-b \sin(t)$
How do I eliminate t to find the Cartesian equation here?
I've tried different weird approaches, i.e. squaring everything and trying to use a trig identity or rearranging and substituing one part of the equation into the other but I'm not getting anywhere and can't eliminate t. I'm not really good when it comes to parametric equations.
Best Answer
$x = a\sin t + b\cos t$
$y = a\cos t - b \sin t$
$x^2 + y^2 = (a\sin t + b\cos t)^2 + (a\cos t - b \sin t)^2$
$x^2 + y^2 = a^2(\sin^2 t + \cos^2t) + b^2(\sin^2 t + \cos^2t) + 2ab\cos t\sin t - 2ab\cos t \sin t$
$$x^2 + y^2 = a^2 + b^2$$