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.