Question

A circle has an area of approximately 78.5 square units. If the center of the circle is at (2,4). Which of the following points is on the circle?

(-6, 4)
(2, -1)
(-4, -4)
(2, -9)

Answer 1

The answer is (2, -1)

The area of the circle is:
A = r²π

We know
A = 78.5
π = 3.14

78.5 = r² * 3.14
r² = 78.5 : 3.15
r² = 25
r = √25 = 5


The standard form equation of a circle is:
(x - h)² + (y - k)² = r²

We have:
(2, 4)
⇒ h = 2
k = 4
r = 5

(x - h)² + (y - k)² = r²
(x - 2)² + (y - 4)² = 5²
(x - 2)² + (y - 4)² = 25

Now, let's substitute all choices:
(-6, 4):
(-6 - 2)² + (2 - 4)² = 25
(-8)² + (-2)² = 25
64 + 4 = 25
68 = 25
INCORRECT

(2, -1)
(2 - 2)² + (-1 -4)² = 25
0² + (-5)² = 25
0 + 25 = 25
25 = 25
CORRECT