For this case we have that the center of the circle is given by the point (4, -3). The radius is [tex]r = 6[/tex]
We find the distance between the center of the circle and the given point by means of the following formula:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]
Let:
[tex](x_ {1}, y_ {1}) = (2, -1)\\(x_ {2}, y_ {2}) = (4, -3)[/tex]
Substituting:
[tex]d = \sqrt {(4-2) ^ 2 + (- 3 - (- 1)) ^ 2}\\d = \sqrt {(2) ^ 2 + (- 3 + 1) ^ 2}\\d = \sqrt {(2) ^ 2 + (- 2) ^ 2}\\d = \sqrt {4 + 4}\\d = \sqrt {8}\\d = 2.828427125[/tex]
The diatnce between the center and the given point is less than the radius of the circle, therefore, the point is inside.
Answer:
Option B
