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

Answer Attempt out of 2
Center:
Radius:
Submit Answer

Ask by Hills Evans. in the United States

Jan 23,2025

Question

Question Find the center and radius of the circle represented by the equation below. $$ (x-8)^{2}+(y+13)^{2}=361 $$ Answer Attempt out of 2 Center: $$ \square $$ Radius: Submit Answer

UpStudy AI · Accepted Answer

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

$$
(x - 8)^2 + (y + 13)^2 = 361
$$

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 the Center $$(h, k)$$:**
   
   - The given equation is $$(x - 8)^2 + (y + 13)^2 = 361$$.
   - Comparing this with the standard form:
     - $$h = 8$$ (since it's $$x - 8$$)
     - $$k = -13$$ (since it's $$y + 13$$, which is equivalent to $$y - (-13)$$)
   
   So, the **center** is $$(8, -13)$$.

2. **Determine the Radius $$r$$:**
   
   - The right side of the equation is $$361$$, which represents $$r^2$$.
   - To find $$r$$, take the square root of $$361$$:
     $$
     r = \sqrt{361} = 19
     $$
   
   So, the **radius** is $$19$$.

**Final Answer:**

- **Center:** $$(8,\ -13)$$
- **Radius:** $$19$$
Center: (8, -13), Radius: 19

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

Answer Attempt out of 2
Center:
Radius:
Submit Answer

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