Final answer:
To find the equation of a circle centered at the origin with points A(9,5) and B(5,-9), we calculate the radius using the distance formula from either point to the origin and use the standard circle equation, resulting in x² + y² = 106.
Step-by-step explanation:
To determine the equation of a circle centered at the origin with points A(9,5) and B(5,-9), we can use the distance formula to find the radius. The distance from either point to the origin (0,0) can serve as the radius, since both points lie on the circle.
For point A, the distance to the origin is:
r = √(9² + 5²) = √(81 + 25) = √106
Since the circle is centered at the origin, the equation of the circle is of the form:
x² + y² = r²
Therefore, substituting our value for r:
x² + y² = 106
This is the equation for the circle.