https://file.aiquickdraw.com/mathbot/file/1727068582369y8kxlcaa.jpg

The image shows the following mathematical expression:

\[
r = \sqrt{2}; \quad (h, k) = (0, 3)
\]

This represents the equation of a circle in standard form, where:
- \( r \) is the radius of the circle, given as \( \sqrt{2} \).
- \( (h, k) \) is the center of the circle, which is at the point \( (0, 3) \).

Using this information, the general equation for a circle is given by:

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

Substituting the values of \( h = 0 \), \( k = 3 \), and \( r = \sqrt{2} \), we get:

\[
(x - 0)^2 + (y - 3)^2 = (\sqrt{2})^2
\]

Simplifying:

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

This is the equation of the circle with a center at \( (0, 3) \) and a radius of \( \sqrt{2} \).

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. How would the equation change if the center was at \( (2, -1) \)?
2. What is the area of the circle based on the given radius?
3. How can we convert the standard form of a circle equation to its general form?
4. How would the equation look if the radius was doubled?
5. What is the length of the diameter of this circle?

**Tip**: The general form of a circle is \( x^2 + y^2 + Dx + Ey + F = 0 \), and it can be derived from the standard form by expanding and rearranging terms.

What is the equation of the circle with radius r = √2 and center (0, 3)?

This tutorial provides a step-by-step solution to finding the equation of a circle with radius √2 and center at (0, 3). It explains the use of the standard circle equation formula: (x - h)^2 + (y - k)^2 = r^2. Ideal for high school students in Grades 9-11.

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