Question

Find the equation of the following curve in cartesian form. If it is a circle, find its centre and radius $x=a+r\cos \alpha ,y=b+r\sin \alpha$

Answer 1

Given $x=a+r\cos \alpha$ and $y=b+r\sin \alpha$.

$(x-a{)}^2+(y-b{)}^2=r^2{\cos }^2\alpha +r^2{\sin }^2\alpha$

$(x-a{)}^2+(y-b{)}^2=r^2({\sin }^2\alpha +{\cos }^2\alpha )$

$(x-a{)}^2+(y-b{)}^2=r^2$ - Cartesian equation.

center $(a,b)$

Radius $=r$.