Final answer:
To find the standard form of the circle's equation, one must determine the center and radius by solving a system of equations derived from the circle passing through the points (0,0), (2.8,0), and (5,2).
Step-by-step explanation:
The question asks to write the standard form of the equation of the circle that passes through three given points, namely the origin, (2.8,0), and (5,2). The standard form for the equation of a circle is (x-h)² + (y-k)² = r², where (h,k) is the center of the circle, and r is the radius.
To find the equation, we need to determine the center and the radius. Since the circle passes through the origin, we can establish a system of equations based on the other two points which the circle passes through. We would end up with two equations:
- (2.8 - h)² + (0 - k)² = r².
- (5 - h)² + (2 - k)² = r².
By solving this system of equations, we can calculate the values of h, k, and r, and then plug these into the standard form equation of a circle.