Participation in the Math Q\&A forums is required for Weeks 3 and 4 . Let $$ (x+3)^{2}+(y-5)^{2}=121 $$. Answer the following questions. a. What does the equation represent? Be specific.

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UpStudy AI · Accepted Answer

The equation $$ (x+3)^{2}+(y-5)^{2}=121 $$ represents a circle in the Cartesian coordinate system.

To break it down:

1. **Standard Form of a Circle**: The standard form of a circle's equation is given by:
   $$
   (x-h)^{2} + (y-k)^{2} = r^{2}
   $$
   where $$ (h, k) $$ is the center of the circle and $$ r $$ is the radius.

2. **Identifying Parameters**:
   - In the given equation, we can identify:
     - $$ h = -3 $$ (the x-coordinate of the center)
     - $$ k = 5 $$ (the y-coordinate of the center)
     - $$ r^{2} = 121 $$, which means $$ r = \sqrt{121} = 11 $$ (the radius of the circle)

3. **Conclusion**: 
   - The center of the circle is at the point $$ (-3, 5) $$.
   - The radius of the circle is $$ 11 $$.

Thus, the equation represents a circle centered at $$ (-3, 5) $$ with a radius of $$ 11 $$.
The equation $$ (x+3)^{2}+(y-5)^{2}=121 $$ represents a circle centered at $$ (-3, 5) $$ with a radius of $$ 11 $$.

Participation in the Math Q\&A forums is required for Weeks 3 and 4 . Let \( (x+3)^{2}+(y-5)^{2}=121 \). Answer the following questions. a. What does the equation represent? Be specific.

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