Question

On a coordinate plane, circle
O
has its center at the point
(
2
,
3
)
. The point
(
−
1
,
−
1
)
is on circle
O
.

Which of these statements are correct?

Choose all that are correct.

A.
The radius of the circle can be found by doubling the distance between
(
2
,
3
)
and
(
−
1
,
−
1
)
.

B.
The equation
(
x
−
2
)
2
+
(
y
−
3
)
2
=
5
describes circle
O
.

C.
The radius of the circle can be found by finding the distance between
(
2
,
3
)
and
(
−
1
,
−
1
)
.

D.
The diameter of the circle can be found by finding the distance between
(
2
,
3
)
and
(
−
1
,
−
1
)
.

E.
The equation
(
x
+
2
)
2
+
(
y
+
3
)
2
=
5
describes circle
O
.

F.
The equation
(
x
−
2
)
2
+
(
y
−
3
)
2
=
25
describes circle
O
.

Answer 1

Correct answers: C and F.

Reasoning: Distance from center (2,3) to point (-1,-1) is sqrt[(-3)^2+(-4)^2] = 5, so the radius is 5. Thus the radius is the distance (C true) and the circle equation is (x−2)^2+(y−3)^2=25 (F true). A and D are wrong because doubling (or taking) that distance gives the diameter, not the radius; B and E give wrong centers or radii.