Question

NO LINKS!! PART 2: Find the EXACT area and Circumference of each circle​

Answer 1

#2

• (x-2)²+(y-5)²=9
• (x-2)²+(y-5)²=3²

Radius=3

Circumference

• 2π(3)
• 6π units

Area

• πr²
• 3²π
• 9π units²

#4

• x²+y²=64
• x²+y²=8²

Radius=8

Circumference

• 2π(8)
• 16π units

Area

• πr²
• π(8)²
• 64π units ²

Answer 2

2. center: (2, 5); radius: 3; Area: 9π; Circumference: 6π

4. center: (0, 0); radius: 8; Area: 64π; Circumference: 16π

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

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2.

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

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4.

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