Question

draw the circle $x^{2}+(y + 3)^{2}=4$.
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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 \(x^{2}+(y + 3)^{2}=4\), we have \(h = 0\), \(k=-3\), and \(r=\sqrt{4}=2\).

Step2: Plot the center

The center of the circle is \((0,-3)\). Mark this point on the coordinate plane.

Step3: Plot points around the center

From the center \((0,-3)\), move 2 units up (to \((0,-1)\)), 2 units down (to \((0,-5)\)), 2 units left (to \((-2,-3)\)), and 2 units right (to \((2,-3)\)).

Step4: Draw the circle

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

Answer:

The circle has center \((0,-3)\) and radius \(2\). Mark the center \((0,-3)\) on the coordinate plane. Then, from the center, move \(2\) units in the up, down, left, and right directions to get the points \((0,-1)\), \((0,-5)\), \((-2,-3)\), and \((2,-3)\). Connect these points (and other points around the center at a distance of \(2\) units) to draw the circle \(x^{2}+(y + 3)^{2}=4\).