Final answer:
The equation of the circle x² + y² = 36 represents a circle centered at the origin (0, 0) with a radius equal to 6 units.
Step-by-step explanation:
The equation of a circle in standard form is (x - h)² + (y - k)² = r², where (h, k) represents the coordinates of the center of the circle, and r is the radius. In the given equation x² + y² = 36, the absence of constants alongside x² and y² indicates that the equation is already in standard form, implying that the center of the circle is at the origin (0, 0).
The equation's form x² + y² = 36 is recognized as the equation of a circle with a radius of 6 units. The radius of a circle is the square root of the constant term on the right side of the equation, which in this case is √36 = 6. Therefore, the circle has a radius of 6 units.
Overall, the equation x² + y² = 36 describes a circle centered at the origin (0, 0) with a radius of 6 units. This standard form of the circle's equation provides information about the center coordinates and the length of the radius, which are crucial elements for understanding and plotting the circle on a coordinate plane.
Complete Question:
The circle with equation x^(2)+y^(2)=36 has center with coordinates and a radius equal to