https://file.aiquickdraw.com/mathbot/file/17269152283452e32n2qj.jpg

We are given two circles, Circle A and Circle B, in the xy-plane with their equations. Here's how we can break it down:

### Circle A:
The equation for Circle A is:
\[
(x + 5)^2 + (y - 5)^2 = 4
\]
This is the standard form of a circle equation \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

- Center of Circle A: \((-5, 5)\)
- Radius of Circle A: \(\sqrt{4} = 2\)

### Circle B:
Circle B has the same center as Circle A but its radius is twice the radius of Circle A. Therefore, the radius of Circle B is:
\[
2 \times 2 = 4
\]
The equation for Circle B is given as:
\[
(x + 5)^2 + (y - 5)^2 = k
\]
Since the radius of Circle B is 4, and the equation of a circle is \((x - h)^2 + (y - k)^2 = r^2\), we can equate \(r^2 = k\):
\[
k = 4^2 = 16
\]

Thus, the value of \(k\) is \(16\).

---

Do you have any questions or would you like more details? Here are some related questions for further practice:

1. How would you write the equation of a circle with a center at \((3, -7)\) and a radius of 5?
2. If Circle A had a radius of 3 instead of 2, what would be the value of \(k\) for Circle B?
3. What would the equation for Circle A be if its radius were halved?
4. How do you find the equation of a circle given three points on its circumference?
5. How does the equation of a circle change when it is translated horizontally by 2 units?

**Tip:** Remember that the general form of a circle's equation is directly tied to its center and radius. Always square the radius for the equation!

Circle A in the xy-plane has the equation (x + 5)^2 + (y - 5)^2 = 4. Circle B has the same center as Circle A. The radius of circle B is two times the radius of circle A. The equation defining circle B in the xy-plane is (x + 5)^2 + (y - 5)^2 = k, where k is a constant. What is the value of k?

Learn how to find the value of k in a circle equation. This problem involves circles in the xy-plane, using the equation (x + 5)^2 + (y - 5)^2 = 4 for Circle A and determining the equation for Circle B when its radius is twice that of Circle A. Ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation