The image you uploaded shows a graph with a circle and a horizontal line. The circle is centered at the origin (0,0) and has a radius of 10, while the red horizontal line appears to be the x-axis (where $y = 0$).

To find the points of intersection between the circle and the line, we can set up the equation of the circle and solve it with the equation of the line.

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

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

For the given circle with center at $(0, 0)$ and radius $r = 10$, the equation is:

$x^2 + y^2 = 10^2$ $x^2 + y^2 = 100$

The red line appears to be $y = 0$ (the x-axis). Substituting $y = 0$ into the equation of the circle:

$x^2 + 0^2 = 100$ $x^2 = 100$ $x = \pm 10$

Thus, the points of intersection are $(10, 0)$ and $(-10, 0)$.

Do you want further details on this? Or would you like to explore related concepts?

Here are some related questions for you:

1. What is the general form of the equation of a circle?
2. How do you find the points of intersection of a circle and a line?
3. What other types of curves intersect with horizontal lines?
4. How do you analyze the intersection of a circle with a vertical line?
5. How would the intersection change if the radius of the circle were different?

Tip: When solving circle equations, always keep in mind the standard form $(x-h)^2 + (y-k)^2 = r^2$ and how it relates to transformations of the circle.