find the equation of a circle ,the end point of whose diameter are( 2 -3 )and(-2,4). Find it's center and radius.
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Step-by-step explanation:
The standard form for the equation of a circle is:
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
where
x
and
y
are any point,
(
x
,
y
)
, on the circle,
(
h
,
k
)
is the center, and r is the radius.
The center of the circle is halfway between the two endpoints, from
(
5
,
8
)
to
(
5
,
−
4
)
:
Δ
x
=
(
5
−
5
)
=
0
Δ
y
=
(
−
4
−
8
)
=
−
12
This means that the center is
−
6
in the vertical direction from the starting point,
(
5
,
8
)
, which brings us to the point
(
5
,
2
)
.
This, also, tells us that the radius is 6.
We have have all of the information that we need to substitute into the standard form:
(
x
−
5
)
2
+
(
y
−
2
)
2
=
6
2
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