Question

(1 pt) Find a vector parametrization of the circle of radius 8 in the xy-plane, centered at (−3,−5), oriented counterclockwise. The point (5,−5) should correspond to t=0. Use t as the parameter in your answer.

Answer 1

`x(t)=8 \cos(t) -3\\\\y(t)=8 \sin(t)-5`

Explanation:

The equation of the circle centered at (-3,-5) in the xy-plane is

`(x+3)^2+(y+5)^2=8^2`

hence in vector parametrization, we have

`x+3=8\cos(t)\\\\y+5=8\sin(t)`

and so

`x(t)=8\cos(t)-3\\\\y(t)=8\sin(t)-5`

Moreover, note that

`x(0)=8\cos(0)-3=8-3=5\\\\y(0)=8\sin(0)-5=0-5=-5`

Otherwise, we should have used a parametrization and we are done.