Question

Find the standard form of the equation of the circle with endpoints of a diameter at the points

(4,8) and (2,6).

Answer 1

(
x
−
1
)
2
+
(
y
−
7
)
2
=
37
Step-by-step explanation:
The center of the circle is the midpoint of the diameter, i.e.
(
7
−
5
2
,
8
+
6
2
)
=
(
1
,
7
)
Again, the diameter is the distance between the points s
(
7
,
8
)
and
(
−
5
,
6
)
:
√
(
7
−
(
−
5
)
)
2
+
(
8
−
6
)
2
=
√
12
2
+
2
2
=
2
√
37
so the radius is
√
37
.
Thus the standard form of the circles equation is
(
x
−
1
)
2
+
(
y
−
7
)
2
=
37