Complete the equation of the circle centered at (-8,2) with radius 3.

To complete the equation of a circle, we use the standard form:

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

Where:
- \((h, k)\) is the center of the circle.
- \(r\) is the radius.

Given:
- Center: \((-8, 2)\) → So, \(h = -8\) and \(k = 2\).
- Radius: \(r = 3\).

Substitute these values into the equation:

\[
(x - (-8))^2 + (y - 2)^2 = 3^2
\]

Simplifying:

\[
(x + 8)^2 + (y - 2)^2 = 9
\]

Thus, the equation of the circle is:

\[
(x + 8)^2 + (y - 2)^2 = 9
\]

Would you like more details or have any questions?

---

Here are 5 related questions to expand on this topic:

1. What is the general equation of a circle if the radius is unknown but the center is given?
2. How do you find the radius of a circle given its equation in standard form?
3. Can a circle have a radius of 0? What would its equation be?
4. How would the equation change if the center was at the origin (0, 0)?
5. How do you find the equation of a circle passing through a specific point?

**Tip:** The distance between any point on the circle and its center is always the radius.

Learn how to complete the equation of a circle with center at (-8, 2) and radius 3 using the standard form of the circle equation: (x - h)^2 + (y - k)^2 = r^2. This geometry problem covers key concepts in coordinate geometry and is ideal for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation