Question

draw the circle $x^{2}+y^{2}=16$. question help: video

Explanation:

Step1: Recall the standard form of a circle

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

Step2: Plot key points

• The center of the circle is at the origin \((0,0)\).
• Points on the circle along the \(x\) - axis: When \(y = 0\), \(x^{2}=16\), so \(x=\pm4\). The points are \((4,0)\) and \((- 4,0)\).
• Points on the circle along the \(y\) - axis: When \(x = 0\), \(y^{2}=16\), so \(y=\pm4\). The points are \((0,4)\) and \((0,-4)\).
• Other points: For example, when \(x = 2\), \(y^{2}=16 - 4=12\), \(y=\pm2\sqrt{3}\approx\pm3.46\). When \(x=-2\), \(y=\pm2\sqrt{3}\approx\pm3.46\).

Step3: Draw the circle

Using the center \((0,0)\) and the radius \(r = 4\), and the key points \((4,0),(-4,0),(0,4),(0,-4)\) (and optionally other calculated points), draw a smooth, round curve passing through these points.

Answer:

The circle has center \((0,0)\) and radius \(4\). Plot the center and the points \((4,0),(-4,0),(0,4),(0,-4)\) and draw a smooth curve through them.