Answer:
2. center: (2, 5); radius: 3; Area: 9π; Circumference: 6π
4. center: (0, 0); radius: 8; Area: 64π; Circumference: 16π
Step-by-step explanation:
The standard form equation for a circle is ...
(x -h)² +(y -k)² = r² . . . . . . center (h, k), radius r
The value of r is used in the formulas for area (A) and circumference (C):
A = πr²
C = 2πr
__
<h3>2.</h3>
Comparing the given equation to the standard form, we see ...
(x -h)² +(y -k)² = r²
(x -2)² +(y -5)² = 9
(h, k) = (2, 5) . . . . center
r² = 9
This tells us ...
r = √9 = 3 . . . . radius
The Area formula uses r² directly:
Area = πr² = π(9)
Area = 9π
The Circumference formula uses r:
Circumference = 2π(3)
Circumference = 6π
__
<h3>4.</h3>
Comparing the given equation to the standard form, we find ...
(h, k) = (0, 0) . . . . center
r² = 64 ⇒ r = √64 = 8 . . . . radius
Area = 64π
Circumference = 2π(8) = 16π
