Write the standard equation for the circle that passes through the points (- 5, 0), (0, 4), and (2, 4).
1 answer:
Answer:
x
2
+
y
2
−
6
x
+
4
y
−
37
=
0
Explanation:
let's substitute each coordinate of all points in the general equation of the circle:
x
2
+
y
2
+
a
x
+
b
y
+
c
=
0
so that you have three equations with unknown variables a,b,c:
4
2
+
5
2
+
4
a
+
5
b
+
c
=
0
and
(
−
2
)
2
+
3
2
−
2
a
+
3
b
+
c
and
(
−
4
)
2
+
(
−
3
)
2
−
4
a
−
3
b
+
c
=
0
let's solve in a few steps:
4
a
+
5
b
+
c
+
41
=
0
and
−
2
a
+
3
b
+
c
+
13
=
0
and
−
4
a
−
3
b
+
c
+
25
=
0
c
=
−
4
a
−
5
b
−
41
and
(by substituting c)
−
2
a
+
3
b
−
4
a
−
5
b
−
41
+
13
=
0
and
−
4
a
−
3
b
−
4
a
−
5
b
−
41
+
25
=
0
−
6
a
−
2
b
−
28
=
0
and
−
8
a
−
8
b
−
16
=
0
that is equivalent to:
3
a
+
b
+
14
=
0
and
a
+
b
+
2
=
0
By subtracting you obtain:
2
a
+
12
=
0
a
=
−
6
so, by substituting the obtained value of a:
−
6
+
b
+
2
=
0
b
=
4
so
c
=
−
4
(
−
6
)
−
5
(
4
)
−
41
=
24
−
20
−
41
=
−
37
The equation of the circle is:
x
2
+
y
2
−
6
x
+
4
y
−
37
=
0
Step-by-step explanation:
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