Write an equation of the circle with the given center and radius.
​(minus3​,4​); requalsStartRoot 2 EndRoot
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Part 1
The equation is 
  
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The equation of a circle with a given center \((h, k)\) and radius \(r\) is:

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

Given the center \((-3, 4)\) and radius \(r = \sqrt{2}\), we can plug these values into the formula:

\[
(x - (-3))^2 + (y - 4)^2 = (\sqrt{2})^2
\]

Simplifying this, we get:

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

So, the equation of the circle is:

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

Would you like more details or have any questions?

Here are some related questions you might find useful:

1. How do you determine the radius of a circle from its equation?
2. What is the general form of a circle's equation, and how does it differ from the standard form?
3. How do you find the center and radius from a given equation of a circle?
4. Can a circle's equation have complex numbers? If so, how would it be written?
5. How does the equation of a circle change if it is shifted along the x-axis or y-axis?

**Tip:** Always double-check the signs when substituting the center's coordinates into the circle's equation to avoid common mistakes.

Learn how to write the equation of a circle with center (-3, 4) and radius √2. This problem involves coordinate geometry and circle equations. Suitable for high school students studying geometry and algebra.

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