The image you've uploaded shows a circle on a coordinate grid, with point $A$ marked at the center. The radius of the circle is shown as 1 unit. It appears that the question is asking for the equation of the circle.

Solution:

Given:

• The center of the circle $A$ is at the origin (0, 0) because it's aligned with the intersection of the x-axis and y-axis.
• The radius $r$ of the circle is given as 1 unit.

The general equation of a circle with center at $(h, k)$ and radius $r$ is:

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

Here, since the center $A$ is at $(0, 0)$, the equation simplifies to:

$x^2 + y^2 = r^2$

Substituting $r = 1$ into the equation:

$x^2 + y^2 = 1$

So, the correct answer is:

$\boxed{x^2 + y^2 = 1}$

Would you like further details on this solution or have any other questions?

Related Questions:

1. How would the equation change if the radius were 2 units?
2. What would be the equation if the center of the circle was at $(1, 2)$ instead of $(0, 0)$?
3. How do you find the radius from the equation of a circle?
4. What is the area of the circle with radius 1?
5. How does the equation of a circle differ from that of an ellipse?

Tip:

Always double-check the center and radius when determining the equation of a circle—small errors here can lead to incorrect answers.