Question

what is the equation of this circle in standard form?
○ $(x - 1)^2+(y + 1)^2=5$
○ $(x + 1)^2+(y - 1)^2=25$
○ $(x + 1)^2+(y - 1)^2=5$
○ $(x - 1)^2+(y + 1)^2=25$

Explanation:

Step1: Recall the standard form of a circle equation

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.

Step2: Identify the center and radius from the graph

From the graph, the center \((h,k)=(1, - 1)\) (approximate by observing the position of the center point). The radius \(r = 5\) (by measuring the distance from the center to a point on the circle, for example, from \((1,-1)\) to \((6,-1)\) the distance is \(|6 - 1|=5\)).

Step3: Substitute \(h = 1\), \(k=-1\), \(r = 5\) into the standard form

Substituting into \((x - h)^2+(y - k)^2=r^2\), we get \((x - 1)^2+(y+1)^2=25\)

Answer:

\((x - 1)^2+(y + 1)^2=25\)