Final answer:
A unique circle equation cannot be determined with only a single point provided; additional information such as the center or radius of the circle is necessary.
Step-by-step explanation:
The question asks to find the equation of a circle passing through a given point (5, 8). The general equation for a circle with center (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2. Since only one point is given, there can be an infinite number of circles that pass through that point, each with different centers and radii. To find a specific circle's equation, more information is required, such as the circle's center or radius. Without additional information, we cannot determine a unique equation for the circle.
The equation of a circle centered at (h, k) with radius r is given by:(x - h)^2 + (y - k)^2 = r^2Since the circle passes through the point (5, 8), we can substitute these values into the equation to find the equation of the circle. Assuming the center of the circle is (h, k), we have:(5 - h)^2 + (8 - k)^2 = r^2.