The equation of the circle can be shown as, x² + y² = 9², or, x² + y² = 81.
The equation of a circle, with the center at the origin and the radius r units, is given as x² + y² = r².
In the question, we are asked to write the equation for a circle centered at the origin with x-intercepts of (-9, 0) and (9, 0).
We can find the radius of the circle using the distance formula,
D = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁, y₁) and (x₂, y₂) are the endpoints of a line segment.
Radius is the distance between the center and any point on the circle.
Thus, taking (x₁, y₁) as (0, 0), the origin, for the center, and (x₂, y₂) as (9, 0), for any point on the circle, we get the radius as:
r = √((9 - 0)² + (0 - 0)²),
or, r = √(9² + 0²),
or, r = √9² = 9.
Thus, the radius of the circle is r = 9 units.
Thus, the equation of the circle can be shown as, x² + y² = 9², or, x² + y² = 81.
Learn more about the equation of the circle at
https://brainly.com/question/3453918
#SPJ1
