To determine which points lie on the given circle, we start with the equation of a circle in standard form:
(x – h)² + (y – k)² = r²
In this case, the center of the circle is at P(6, 1), so h = 6 and k = 1. The radius r is given as 5 units. Plugging these values into the equation gives us:
(x – 6)² + (y – 1)² = 5²
This simplifies to:
(x – 6)² + (y – 1)² = 25
Now, we need to find points (x, y) that satisfy this equation. For example, if we want to find a specific point, let’s take:
- Point A: (6, 6)
Plugging this point into our circle equation:
(6 – 6)² + (6 – 1)² = 0 + 25 = 25
Since this holds true, point A (6, 6) is indeed on the circle.
Other points can be found similarly by using different x or y values that maintain the equality.