The problem asks for the equation of a circle centered at the origin $(0, 0)$ that passes through the point $(-5, 0)$.

1. Problem Description

The problem asks for the equation of a circle centered at the origin $(0, 0)$ that passes through the point $(-5, 0)$.

2. Solution Steps

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

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

Since the circle is centered at the origin $(0, 0)$, we have $h = 0$ and $k = 0$. The equation becomes:

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

The circle passes through the point $(-5, 0)$. We can substitute these coordinates into the equation to find the radius $r$:

$(-5)^2 + (0)^2 = r^2$

$25 + 0 = r^2$

$r^2 = 25$

$r = \sqrt{25} = 5$

Therefore, the equation of the circle is:

$x^2 + y^2 = 25$

3. Final Answer

$x^2 + y^2 = 25$