Question
Find the center and radius of the circle represented by the equation below.

Answer Attempt 2 out of 2
Center:
Radius:

Ask by Long Elliott. in the United States

Jan 23,2025

Question

Question Find the center and radius of the circle represented by the equation below. $$ (x+8)^{2}+(y-1)^{2}=169 $$ Answer Attempt 2 out of 2 Center: Radius:

UpStudy AI · Accepted Answer

To find the **center** and **radius** of the circle represented by the equation:

$$
(x + 8)^{2} + (y - 1)^{2} = 169
$$

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.

**Step-by-Step Solution:**

1. **Identify the Values:**
   - Comparing $$(x + 8)$$ with $$(x - h)$$, we see that $$h = -8$$.
   - Comparing $$(y - 1)$$ with $$(y - k)$$, we see that $$k = 1$$.
   - The right side of the equation is $$169$$, which represents $$r^{2}$$. So, $$r = \sqrt{169} = 13$$.

2. **Determine the Center and Radius:**
   - **Center $$(h, k)$$:** $$(-8, 1)$$
   - **Radius $$r$$:** $$13$$

**Final Answer:**

- **Center:** $$(-8, \ 1)$$
- **Radius:** $$13$$
Center: (-8, 1), Radius: 13

Question
Find the center and radius of the circle represented by the equation below.

Answer Attempt 2 out of 2
Center:
Radius:

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Question Find the center and radius of the circle represented by the equation below. Answer Attempt 2 out of 2 Center: Radius: