Find the center and radius of this circle: $$ \begin{array}{c}(x+9)^{2}+(y-6)^{2}=25 \ ext { Center }=([?],[\quad]) \ ext { Radius }=[\quad]\end{array} $$

Question

Find the center and radius of this circle: $$ \begin{array}{c}(x+9)^{2}+(y-6)^{2}=25 \ 	ext { Center }=([?],[\quad]) \ 	ext { Radius }=[\quad]\end{array} $$

UpStudy AI · Accepted Answer

**Step 1: Identify the Equation Components**

The given circle equation is

$$
(x+9)^2 + (y-6)^2 = 25.
$$

This equation is in the standard form

$$
(x-h)^2 + (y-k)^2 = r^2,
$$

where $$(h,k)$$ is the center and $$r$$ is the radius of the circle.

---

**Step 2: Find the Center**

Comparing the given equation with the standard form:

- The term $$(x+9)^2$$ can be seen as $$(x-(-9))^2$$.
- The term $$(y-6)^2$$ is already in the form $$(y-6)^2$$.

Thus, the center $$(h, k)$$ is:

$$
h = -9 \quad \text{and} \quad k = 6.
$$

So, the center is $$\boxed{(-9, \, 6)}$$.

---

**Step 3: Find the Radius**

The right-hand side of the equation is $$25$$, which corresponds to $$r^2$$. Therefore,

$$
r^2 = 25.
$$

Taking the square root of both sides,

$$
r = \sqrt{25} = 5.
$$

---

**Final Answer:**

- Center $$ = (-9, 6) $$
- Radius $$ = 5 $$
Center: (-9, 6), Radius: 5

Find the center and radius of this circle: \( \begin{array}{c}(x+9)^{2}+(y-6)^{2}=25 \\ \text { Center }=([?],[\quad]) \\ \text { Radius }=[\quad]\end{array} \)

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