The equation of the circle passing through the origin and cut of intercept -6 and 4on the Axes
Answers
Solution
A general equation of the circle having center
(
−
g
,
−
f
)
and radius
√
g
2
+
f
2
−
c
looks like
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
Since this passes through the origin,
c
=
0
Case 1: x intercept
=
3
, y intercept
=
4
This case has 4 subcases, namely
a. The circle passes through
(
−
3
,
0
)
and
(
0
,
4
)
Equation becomes
x
2
+
y
2
+
3
x
−
4
y
=
0
b. The circle passes through
(
−
3
,
0
)
and
(
0
,
−
4
)
Equation becomes
x
2
+
y
2
+
3
x
+
4
y
=
0
c. The circle passes through
(
3
,
0
)
and
(
0
,
4
)
Equation becomes
x
2
+
y
2
−
3
x
−
4
y
=
0
d. The circle passes through
(
3
,
0
)
and
(
0
,
−
4
)
Equation becomes
x
2
+
y
2
−
3
x
+
4
y
=
0
Case 2: x intercept
=
4
, y intercept
=
3
This case also has 4 subcases, as below:
a. The circle passes through
(
−
4
,
0
)
and
(
0
,
3
)
Equation becomes
x
2
+
y
2
+
4
x
−
3
y
=
0
b. The circle passes through
(
−
4
,
0
)
and
(
0
,
−
3
)
Equation becomes
x
2
+
y
2
+
4
x
+
3
y
=
0
c. The circle passes through
(
4
,
0
)
and
(
0
,
3
)
Equation becomes
x
2
+
y
2
−
4
x
−
3
y
=
0
d. The circle passes through
(
4
,
0
)
and
(
0
,
−
3
)
Equation becomes
x
2
+
y
2
−
4
x
+
3
y
=
0