Answer:
The circle's equation with center at the origin and radius 3 is:
OC. x² + y² = 9
Explanation:
Step 1: Understand the formula for the equation of a circle.
The general equation of a circle with center (h, k) and radius r is:
(x - h)² + (y - k)² = r²
Step 2: Identify the center and radius of the given circle.
The problem states that the circle is centered at the origin, which means the center coordinates are (0, 0). The radius of the circle is given as 3.
Step 3: Substitute the values into the equation.
Using the formula for the equation of a circle, we substitute the center coordinates and the radius:
(x - 0)² + (y - 0)² = 3²
x² + y² = 9
Step 4: Simplify the equation.
Since the center is at the origin, the coordinates (0, 0) simplify to 0. We are left with:
x² + y² = 9
Therefore, the equation of the given circle is:
x² + y² = 9
This equation represents all the points on the circle with a center at the origin and a radius of 3.