Question

draw the circle ((x - 1)^2 + (y + 2)^2 = 9).
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Explanation:

Step1: Identify the center and radius

The standard form of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.
For the equation \((x - 1)^2+(y + 2)^2=9\), we have \(h = 1\), \(k=-2\), and \(r^2 = 9\) (so \(r = 3\)).

Step2: Plot the center

Plot the point \((1,-2)\) on the coordinate plane.

Step3: Plot points around the center

From the center \((1,-2)\), move 3 units up (to \((1,1)\)), 3 units down (to \((1,-5)\)), 3 units left (to \((-2,-2)\)), and 3 units right (to \((4,-2)\)).

Step4: Draw the circle

Connect these four points (and other intermediate points if needed) to form a smooth circle.

Answer:

Center at \((1,-2)\) with radius \(3\). Plot the center, then points \(3\) units in all directions and draw the circle.