Question

Express the following equation of the curve in cartesian form. If the curve is a circle find its center and radius
i) $x=5\cos \theta ,y=5\sin \theta$
ii) $x=2+3\cos \theta ,y=3-3\sin \theta$

Answer 1

i) $x=5\cos \theta y=5\sin \theta$

$x^2+y^2=25({\cos }^2\theta +{\sin }^2\theta )$

$x^2+y^2=25$

Center $(0,0)$ Radius $=\sqrt{25}=5$

ii) $x=2+3\cos \theta y=3-3\sin \theta$

$(x-2{)}^2+(y-3{)}^2=9({\cos }^2\theta +{\sin }^2\theta )$

$(x-2{)}^2+(y-3{)}^2=9$

Center $(2,3)$ Radius $\sqrt{9}=3$