Question

draw the circle $x^{2}+y^{2}=16$.

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 \(x^{2}+y^{2}=16\), we can rewrite it as \((x - 0)^2+(y - 0)^2 = 4^2\). So the center is \((0,0)\) and the radius \(r = 4\).

Step2: Plot key points

• Points on the x - axis: \((4,0)\) and \((- 4,0)\) (since when \(y = 0\), \(x=\pm4\) from \(x^{2}=16\)).
• Points on the y - axis: \((0,4)\) and \((0,-4)\) (since when \(x = 0\), \(y=\pm4\) from \(y^{2}=16\)).

Step3: Sketch the circle

Using the center \((0,0)\) and the four key points \((4,0)\), \((-4,0)\), \((0,4)\), \((0,-4)\), draw a smooth, round circle passing through these points.

Answer:

The circle has center \((0,0)\) and radius \(4\). Plot the center at the origin, then mark points \(4\) units to the left, right, up, and down from the center, and draw a smooth circle through these points.