Find a parametrization of the circle of radius $4$ in the $xy$-plane, centered at $(−5,4)$, oriented counterclockwise. The point $(−1,4)$ should correspond to $t=0$. Use $t$ as the parameter for all of your answers.
Normally $x=r\cos t$ , $y=-r\sin t$ but when the points given , how can I solve ?
On
The circular equation in the xy-plane that satisfies the problem description is
$$(x+5)^2 + (y-4)^2 = 4^2$$
Comparison to the familiar identity $\cos^2 t + \sin^2 t = 1$ leads one to set
$$\frac{x+5}{4} = \cos(t)$$
$$\frac{y-4}{4} = \sin(t)$$
After rearrangement,
$$x(t) = 4\cos(t)-5$$ $$y(t) = 4\sin(t)+4$$
which happens to satisfy the initial conditions: $x(0)=-1$ and $y(0)=4$. It also moves counterclockwise for $t>0$.
remember equation of a circle centered at the origin: (rcos(t), rsin(t)) = f(t)
then just apply the correct transformations, move 5 to the left, 4 up
$\left(4\cos\left(t\right)-5,\ 4\sin\left(t\right)+4\right)$