In the standard form (x+1)^2+(y+1)^2=7 what is the center and radius?

The given equation \((x+1)^2 + (y+1)^2 = 7\) is in the standard form of a circle:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

To find the center and radius:
1. **Center**: Compare the given equation to the standard form.
   - \((x - (-1))^2 + (y - (-1))^2 = 7\)
   - Thus, \(h = -1\) and \(k = -1\).
   - So, the center is \((-1, -1)\).

2. **Radius**: The right-hand side of the equation is \(r^2 = 7\).
   - Take the square root of 7 to find the radius: \(r = \sqrt{7}\).

**Answer**:
- **Center**: \((-1, -1)\)
- **Radius**: \(\sqrt{7}\)

Would you like more details on this solution or have any other questions?

Here are some related questions you might find useful:
1. How do you find the equation of a circle if the center and radius are given?
2. What does the equation of a circle look like if it is centered at the origin?
3. How do you find the length of a chord of a circle given the radius and distance from the center?
4. How do you determine the points where a circle intersects the coordinate axes?
5. What happens to the radius if you multiply the entire equation of a circle by a constant?
6. How do you find the tangent lines to a circle from a given external point?
7. How do you translate the equation of a circle if the circle is moved to a new center?
8. What is the geometric interpretation of the constant term in the standard equation of a circle?

**Tip**: When comparing the equation to the standard form, pay close attention to the signs in front of \(h\) and \(k\). The signs in the equation will be opposite to the coordinates of the center.

Discover how to find the center and radius of the circle given by the equation (x+1)^2 + (y+1)^2 = 7. Understand the standard form of a circle, equations of circles in coordinate geometry, and the method to calculate radius from the equation. Suitable for high school students studying coordinate geometry.

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