Question Find the center and radius of the circle represented by the equation below. $$ (x+3)^{2}+(y+11)^{2}=196 $$ Answer Attempt 1 out of 2 Center: $$ (\square) $$ (o) Watch Video Radius: Submit Answer

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UpStudy AI · Accepted Answer

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

$$
(x + 3)^{2} + (y + 11)^{2} = 196
$$

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 $$h$$ and $$k$$:**
   
   The given equation is:
   
   $$
   (x + 3)^{2} + (y + 11)^{2} = 196
   $$
   
   Rewrite it to match the standard form:
   
   $$
   (x - (-3))^{2} + (y - (-11))^{2} = 196
   $$
   
   From this, we can see that:
   
   $$
   h = -3 \quad \text{and} \quad k = -11
   $$
   
2. **Determine the Radius $$r$$:**
   
   The right side of the equation is $$196$$, which represents $$r^{2}$$:
   
   $$
   r^{2} = 196
   $$
   
   To find $$r$$, take the square root of both sides:
   
   $$
   r = \sqrt{196} = 14
   $$
   
**Final Answer:**

- **Center:** $$(-3, -11)$$
- **Radius:** $$14$$
Center: $$(-3, -11)$$, Radius: $$14$$

Question Find the center and radius of the circle represented by the equation below. \[ (x+3)^{2}+(y+11)^{2}=196 \] Answer Attempt 1 out of 2 Center: \( (\square) \) (o) Watch Video Radius: Submit Answer

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