Give an equation for the curve

Question

If I am given the following: "Parameterize the unit circle centred around $(1,2)$" and I find the parameteric equation

$x=1+cos(t)$

$y=2+sin(t)$

and they then ask me to give an equation to the curve, is the equation just $x^2+ y^2=1$ ?

Answer 1

You have $$ x-1=\cos t \qquad y-2=\sin t $$ so, since $\cos^2t +\sin^2t=1$ : $$ (x-1)^2+(y-2)^2=1 $$ is the cartesian equation.