Question Find the center and radius of the circle represented by the equation below. $$ (x-11)^{2}+(y+4)^{2}=144 $$ Answer Attempt 2 out of 2 Center: Radius:

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To determine the **center** and **radius** of the circle given by the equation:

$$
(x - 11)^2 + (y + 4)^2 = 144
$$

we can compare it to the standard form of a circle's equation:

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

where:
- $$(h, k)$$ is the **center** of the circle.
- $$r$$ is the **radius** of the circle.

**Step-by-Step Solution:**

1. **Identify $$h$$ and $$k$$:**
   - The equation $$(x - 11)^2$$ implies that $$h = 11$$.
   - The equation $$(y + 4)^2$$ can be rewritten as $$(y - (-4))^2$$, which implies that $$k = -4$$.

2. **Determine the Radius $$r$$:**
   - The right side of the equation is $$144$$, which represents $$r^2$$.
   - To find $$r$$, take the square root of $$144$$:
     $$
     r = \sqrt{144} = 12
     $$

**Final Answer:**

- **Center:** $$(11, -4)$$
- **Radius:** $$12$$
Center: (11, -4), Radius: 12

Question Find the center and radius of the circle represented by the equation below. \[ (x-11)^{2}+(y+4)^{2}=144 \] Answer Attempt 2 out of 2 Center: Radius:

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