Question

which of the following is the equation for the circle above?
a. $(x - 3)^2+(y + 4)^2 = 3$
b. $(x - 3)^2+(y + 4)^2 = 9$
c. $(x + 3)^2+(y - 4)^2 = 9$
d. $(x + 4)^2+(y - 3)^2 = 9$

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: Determine the center and radius from the graph

From the graph, the center of the circle is \((- 3,-4)\) (since the center is 3 units to the left of the \(y\) - axis (\(x=-3\)) and 4 units below the \(x\) - axis (\(y =-4\))). The radius \(r = 3\) (by counting the grid units from the center to the edge of the circle).

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

Substitute into \((x - h)^2+(y - k)^2=r^2\). We get \((x-(-3))^2+(y-(-4))^2=3^2\), which simplifies to \((x + 3)^2+(y + 4)^2=9\).

Answer:

B. \((x - 3)^2+(y + 4)^2=9\)