write the standard form of the equation of the circle with the given center and radius. Center (6,2) r=square root of 2

The standard form of the equation of a circle is:

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

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

For the given center \((6, 2)\) and radius \(r = \sqrt{2}\), we substitute into the formula:

\[
(x - 6)^2 + (y - 2)^2 = (\sqrt{2})^2
\]

Since \((\sqrt{2})^2 = 2\), the equation becomes:

\[
(x - 6)^2 + (y - 2)^2 = 2
\]

This is the standard form of the equation of the circle.

Would you like a deeper explanation of any part? Here are five related questions:

1. What is the general form of the equation of a circle?
2. How do you derive the radius from a given equation of a circle?
3. What if the radius is a negative value?
4. How do you find the center of a circle given its equation in standard form?
5. Can you convert this circle's equation to general form?

**Tip:** The square of the radius (\(r^2\)) is always positive, regardless of whether \(r\) is positive or negative.

Write the standard form of the equation of the circle with the given center and radius. Center (6,2), r = square root of 2.

Learn how to write the standard form of the equation of a circle with the center at (6,2) and radius √2. This geometry problem focuses on the formula (x - h)^2 + (y - k)^2 = r^2, providing a detailed explanation for students in Grades 9-10.

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