Final answer:
The circumference of the circle is found using the formula 2πr, resulting in 12π units, and the area is found with πr², resulting in 36π square units, based on the given equation x² + y² = 36.
Step-by-step explanation:
To find the circumference and area of a circle given the equation x²+y² = 36, we first identify the radius of the circle. In this equation, the number 36 is actually the square of the radius (r²), which means the radius (r) is the square root of 36, or r=6.
The circumference of a circle is calculated using the formula 2πr. Substituting our radius value, we have:
Circumference = 2π(6)
Circumference = 12π
To find the area of the same circle, the formula πr² is used. Again, substituting the radius, we get:
Area = π(6)²
Area = 36π
So, the circumference of the circle is 12π, and the area is 36π. These dimensions aid in understanding geometric properties and calculating various parameters of the circle.