find the equation of the circle with center(-3÷2,1÷2)and diameter 2.
Answers
Answer:
Step-by-step explanation:To find the equation of a circle, we need to find the radius as well as the center.
Since we have the endpoints of the diameter, we can use the midpoint formula to obtain the midpoint, which also happens to be the center of the circle.
Finding the midpoint:
M
=
(
2
+
(
−
3
)
2
,
−
3
+
5
2
)
=
(
−
1
2
,
1
)
So the center of the circle is
(
−
1
2
,
1
)
Finding the radius:
Since we have the endpoints of the diameter, we can apply the distance formula to find the length of the diameter. Then, we divide the length of the diameter by 2 to obtain the radius. Alternatively, we can use the the co-ordinates of the center and one of the endpoints to find the length of the radius (I'll leave this to you - the answers will be the same).
A
B
=
√
(
2
−
(
−
3
)
)
2
+
(
−
3
−
5
)
2
∴
A
B
=
√
89
r
a
d
i
u
s
=
√
89
2
The general equation of a circle is given by:
(
x
−
a
)
2
+
(
y
−
b
)
2
=
r
2
So we have,
(
x
−
(
−
1
2
)
)
2
+
(
y
−
1
)
2
=
(
√
89
2
)
Therefore, the equation of the circle is
(
x
+
1
2
)
2
+
(
y
−
1
)
2
=
89
4