The graph of a circle with center
(x, y) = (3, 4)
is shown below. Write the equation for the circle.

The equation of a circle with a center at \((h, k)\) and radius \(r\) is given by:

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

Given:
- Center \((h, k) = (3, 4)\)

So the equation becomes:

\[
(x - 3)^2 + (y - 4)^2 = r^2
\]

To complete the equation, we need the radius \(r\). If you have information about the radius or a point on the circle, please provide it. Otherwise, the general form is as shown above.

Would you like to provide more details, or do you have any questions?

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Here are 5 related questions to expand on this topic:
1. How do you find the radius of the circle if a point on the circle is given?
2. What is the significance of the center in the equation of a circle?
3. How would the equation change if the center of the circle was moved to the origin \((0, 0)\)?
4. How do you graph a circle given its equation?
5. What happens to the circle if the radius \(r\) is doubled?

**Tip:** When writing the equation of a circle, always identify the center and the radius first.

Learn how to write the equation of a circle with center (3, 4) and explore its properties. This problem involves circle geometry, focusing on the equation (x - 3)^2 + (y - 4)^2 = r^2. Suitable for high school students.

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