Question

Write the equation of circle with the following characteristics: Center at (5,8) and Radius of 5

Answer 1

(
x
+
5
)
2
+
(
y
−
1
)
2
=
26
Explanation:
A circle of radius
r
, centered at
(
h
,
k
)
has the form
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
.
From the given information, we have
h
=
−
5
and
k
=
1
. To find
r
, we need only find the distance from the center
(
h
,
k
)
to a point on the circle. As
(
0
,
0
)
is such a point, applying the distance formula gives us
r
=
√
(
−
5
−
0
)
2
+
(
1
−
0
)
2
=
√
26
Thus the desired equation is
(
x
−
(
−
5
)
)
2
+
(
y
−
1
)
2
=
√
26
2
or, simplifying,
(
x
+
5
)
2
+
(
y
−
1
)
2
=
26