The given circle is shown on a coordinate plane, and we are tasked with finding its standard form equation.

The standard form of a circle's equation is:

$(x - h)^2 + (y - k)^2 = r^2$ Where:

• $(h, k)$ is the center of the circle.
• $r$ is the radius.

From the graph:

• The center of the circle appears to be at $(-5, -5)$.
• The radius is the distance from the center to the edge of the circle. By counting the grid squares, it looks like the radius is $5$ units.

Substituting these values into the standard form equation:

$(x - (-5))^2 + (y - (-5))^2 = 5^2$ This simplifies to: $(x + 5)^2 + (y + 5)^2 = 25$

Final Answer:

The standard form of the equation for the given circle is: $(x + 5)^2 + (y + 5)^2 = 25$

Let me know if you need further explanation or have questions about any step!

Here are 5 related questions for practice:

1. How do you find the radius of a circle from its equation?
2. What is the general form of a circle's equation, and how does it relate to the standard form?
3. How do you calculate the distance between two points in the coordinate plane?
4. If the circle was centered at the origin, what would its equation look like?
5. How would the equation change if the radius were doubled?

Tip: Always ensure you clearly identify the center and radius when dealing with circles on a graph.