Question

write the standard equation of ⊙p shown to the right. the standard form of the equation of the circle is (type an equation. simplify your answer.)

Explanation:

1. Recall the standard - form equation of a circle:

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

1. Determine the center and radius from the graph:

• From the graph, the center of the circle \(P\) is \((- 3,2)\), so \(h=-3\) and \(k = 2\).
• The radius \(r\) of the circle can be found by counting the distance from the center to a point on the circle. For example, the distance from the center \((-3,2)\) to the point \((-3, - 1)\) (a point on the circle directly below the center) is \(r=3\).

1. Substitute the values of \(h\), \(k\), and \(r\) into the standard - form equation:

• Substituting \(h=-3\), \(k = 2\), and \(r = 3\) into \((x - h)^2+(y - k)^2=r^2\), we get \((x+3)^2+(y - 2)^2=9\).

Answer:

\((x + 3)^2+(y - 2)^2=9\)