Question

draw the circle $x^2 + y^2 = 9$.
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Explanation:

Step1: Identify the center and radius of the circle

The standard form of a circle equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.
For \(x^{2}+y^{2}=9\), we can rewrite it as \((x - 0)^2+(y - 0)^2 = 3^2\). So the center is \((0,0)\) and the radius \(r = 3\).

Step2: Plot key points

• When \(x = 0\), \(y^{2}=9\), so \(y=\pm3\). The points are \((0,3)\) and \((0, - 3)\).
• When \(y = 0\), \(x^{2}=9\), so \(x=\pm3\). The points are \((3,0)\) and \((-3,0)\).

Step3: Draw the circle

Using the center \((0,0)\) and the four key points \((3,0)\), \((-3,0)\), \((0,3)\), \((0, - 3)\), sketch a smooth - curved circle.

Answer:

Using the center \((0,0)\) and radius \(r = 3\), plot the points \((3,0)\), \((-3,0)\), \((0,3)\), \((0, - 3)\) and draw a smooth - curved circle.