Question

find parametric equations that define the curve with a counter - clockwise orientation starting and ending at (3,0) as shown. the parametric equations that describe exactly one instance of the given curve on the interval ( 0leq tleq2pi ) are ( x=square ), ( y=square ).

Explanation:

Step1: Determine the center and radius of the circle

From the graph, the center of the circle is \((0, - 3)\) and the radius \(r = 2\).

Step2: Recall the general parametric equations for a circle

The general parametric equations for a circle with center \((h,k)\) and radius \(r\) are \(x=h + r\cos t\) and \(y = k+r\sin t\), where \(t\in[0,2\pi]\).

Step3: Substitute the values of \(h\), \(k\), and \(r\) into the equations

Here, \(h = 0\), \(k=-3\), and \(r = 2\).
So, \(x=0 + 2\cos t=2\cos t\) and \(y=-3 + 2\sin t\).

Answer:

\(x = 2\cos t\), \(y=-3 + 2\sin t\)