What is the minimum distance of the circle given by the equation                                                            from the coordinate axes?
A) 5
B) 1
C) 2
D) 4
E) 3


To find the minimum distance of a circle from the coordinate axes, we first need to determine the circle's center. The general equation of a circle is:

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

where \((h, k)\) is the center of the circle and \(r\) is its radius.

However, you've mentioned an equation without providing it explicitly. So, I'll explain the process for finding the minimum distance of a circle from the coordinate axes once you provide the circle's equation.

### Steps to Find the Minimum Distance

1. **Identify the center** \((h, k)\) of the circle from its equation.
2. **Calculate the minimum distance** from the center to the x-axis, which is \(|k|\).
3. **Calculate the minimum distance** from the center to the y-axis, which is \(|h|\).
4. The minimum distance of the circle from the coordinate axes will be the smaller of \(|h|\) or \(|k|\).

If you provide the specific equation of the circle, I can calculate the exact minimum distance for you!

### Follow-Up Questions

1. What is the equation of the circle in your problem?
2. How do you find the center of a circle from its equation?
3. What is the general formula for the distance between a point and a line?
4. How do you determine the radius of a circle from its equation?
5. What methods are used to convert the general form of a circle's equation to the standard form?

**Tip:** Knowing the standard form of a circle's equation helps quickly identify its geometric properties like center and radius.

What is the minimum distance of the circle given by the equation from the coordinate axes?
A) 5
B) 1
C) 2
D) 4
E) 3

Explore how to find the minimum distance of a circle from the coordinate axes using the circle equation. Learn key geometric concepts and formulas, such as the distance from a point to a line. Suitable for students in Grades 8-10.

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