This image asks for graphing the circle given by the equation:

$(x + 4)^2 + (y + 7)^2 = 1.$

Key Details:

1. Center of the Circle: The equation is written in the standard form of a circle: $(x - h)^2 + (y - k)^2 = r^2,$ where $(h, k)$ is the center and $r$ is the radius. Here:

   • $h = -4$ (opposite sign of $+4$),
   • $k = -7$ (opposite sign of $+7$), so the center is $(-4, -7)$.

2. Radius: From the equation $r^2 = 1$, the radius is: $r = \sqrt{1} = 1.$

Graphing Instructions:

• Plot the Center: Place a point at $(-4, -7)$.
• Draw the Circle: Use the radius $r = 1$ to draw a circle around $(-4, -7)$, ensuring all points are equidistant from the center by 1 unit.

Would you like me to provide a detailed example of graphing circles or explain related concepts?

Here are some related questions you might explore:

1. What happens to the circle if the radius increases or decreases?
2. How does shifting the center affect the graph of the circle?
3. Can the circle's equation be written differently, such as expanded?
4. How do you calculate the area and circumference of this circle?
5. How can circles be represented parametrically?

Tip: Always confirm the center and radius directly from the equation to avoid sign errors.