Question

circles
identify the center and radius of each. then sketch the graph.

1. $(x + 2)^2+(y - 1)^2=9$
2. $(x + 3)^2+(y + 4)^2=3$
3. $(x - 2)^2+(y + 3)^2=1$
4. $x^2 + y^2-6y = 0$
5. $x^2 + y^2+4x + 2y-4 = 0$
6. $x^2 + y^2-4x-14 = 0$

Explanation:

Step1: Recall circle - standard form

The standard form of a circle is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center and $r$ is the radius.

Step2: For $(x + 2)^2+(y - 1)^2=9$

Center is $(-2,1)$, radius $r = 3$.

Step3: For $(x + 3)^2+(y + 4)^2=3$

Center is $(-3,-4)$, radius $r=\sqrt{3}$.

Step4: For $(x - 2)^2+(y + 3)^2=1$

Center is $(2,-3)$, radius $r = 1$.

Step5: For $x^{2}+y^{2}-6y = 0$

Complete the square: $x^{2}+(y - 3)^2=9$. Center is $(0,3)$, radius $r = 3$.

Step6: For $x^{2}+y^{2}+4x + 2y-4 = 0$

Complete the square: $(x + 2)^2+(y + 1)^2=9$. Center is $(-2,-1)$, radius $r = 3$.

Step7: For $x^{2}+y^{2}-4x-14 = 0$

Complete the square: $(x - 2)^2+y^{2}=18$. Center is $(2,0)$, radius $r = 3\sqrt{2}$.

Answer:

1. Center: $(-2,1)$, Radius: $3$
2. Center: $(-3,-4)$, Radius: $\sqrt{3}$
3. Center: $(2,-3)$, Radius: $1$
4. Center: $(0,3)$, Radius: $3$
5. Center: $(-2,-1)$, Radius: $3$
6. Center: $(2,0)$, Radius: $3\sqrt{2}$