Question

10 multiple choice 1 point what is the equation of this circle? $(x - 1)^{2}+(y - 3)^{2}=4$ $x^{2}+(y + 3)^{2}=16$ $x^{2}+(y - 3)^{2}=16$ $(x - 3)^{2}+y^{2}=16$

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Identify the center and radius from the graph

From the graph, the center \((h,k)=(0,3)\) (since it's on the \(y\) - axis, \(x = 0\) and \(y=3\)). The radius \(r = 4\) (distance from center \((0,3)\) to the \(x\) - axis).

Step3: Substitute \(h = 0\), \(k = 3\), and \(r = 4\) into the standard form

Substituting into \((x - h)^2+(y - k)^2=r^2\), we get \((x-0)^2+(y - 3)^2=4^2\), which simplifies to \(x^{2}+(y - 3)^2=16\).

Answer:

\(x^{2}+(y - 3)^2=16\) (the third option)