Question

Find the equation of the following curve in cartesian form $x=-1+2\sin \theta ,y=1+2\cos \theta .$ find the centre and radius of circle.

Answer 1

$x=-1+2sin\theta$

$y=1+2cos\theta$

$(x+1{)}^2+(y-1{)}^2=4si{n}^2\theta +4co{s}^2\theta$

$(x+1{)}^2+(y-1{)}^2=4(si{n}^{2\theta }+co{s}^2\theta )$

$(x+1{)}^2+(y-1{)}^2=4$

$(x+1{)}^2+(y-1{)}^2=2^2$

centre $(-1,1)$, Radius=$2$.