Observe the graph:

The circle in the graph is located at second and third quadrants and center is passes through -axis.

Standard form of circle equation is , where is center and is radius.

Determine which of the below equations are in second and third quadrants and center is passes through -axis.

Write each equation in standard form.

Check the sign of -coordinate is negative and -coordinate is zero.

(a). The circle equation is .

Compare it with standard form of circle equation is .

The -coordinate of center of the circle is positive and -coordinate is zero.

(b). The circle equation is .

Compare it with standard form of circle equation is .

The -coordinate of center of the circle is negative and -coordinate is zero.

(c). The circle equation is .

Compare it with standard form of circle equation is .

The -coordinate of center of the circle is zero and -coordinate is two.

(d). The circle equation is .

Compare it with standard form of circle equation is .

The -coordinate of center of the circle is negative and -coordinate is zero.  

(e). The circle equation is .

By using completing square method convert the below equations in to standard form of circle.

To change expression in to a perfect square trinomials add   to each side of expressions.

Compare it with standard form of circle equation is .

The -coordinate of center of the circle is negative and -coordinate is zero.

(f). The circle equation is .

Compare it with standard form of circle equation is .

The -coordinate of center of the circle is negative and -coordinate is one.

(g). The circle equation is .

Compare it with standard form of circle equation is .

The -coordinate of center of the circle is negative and -coordinate is zero.

(h). The circle equation is .

Compare it with standard form of circle equation is .

The -coordinate of center of the circle is negative and -coordinate is zero.

Possible equations are (b), (d), (e), (g).