Problem

(1 point) The circle $(x-9)^{2}+(y-6)^{2}=4$ can be drawn with parametric equations. Assume the circle is traced clockwise as the parameter increases. If $x=9+2 \cos t$ then $y=$

Solution

Step 1 :The general form of the parametric equations for a circle centered at \((h, k)\) with radius \(r\) is \(x = h + r \cos t\) and \(y = k - r \sin t\) if the circle is traced clockwise.

Step 2 :In this case, the center of the circle is at \((9, 6)\) and the radius is \(2\).

Step 3 :Therefore, we can substitute these values into the equation for \(y\) to find the parametric equation for \(y\).

Step 4 :Let \(t = t\), \(h = 9\), \(k = 6\), and \(r = 2\).

Step 5 :Substituting these values into the equation for \(y\), we get \(y = 6 - 2 \sin t\).

Step 6 :Final Answer: \(\boxed{y = 6 - 2 \sin t}\)

From Solvely APP
Source: https://solvelyapp.com/problems/lW6KL90tKg/

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