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Mathematics
Problem
If the circle
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
x^2 + y^2 + 2gx + 2fy + c = 0
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
cuts each of the circles
x
2
+
y
2
−
4
=
0
x^2 + y^2 - 4 = 0
x
2
+
y
2
−
4
=
0
,
x
2
+
y
2
−
6
x
−
8
y
+
10
=
0
x^2 + y^2 - 6x - 8y + 10 = 0
x
2
+
y
2
−
6
x
−
8
y
+
10
=
0
and
x
2
+
y
2
+
2
x
−
4
y
−
2
=
0
x^2 + y^2 + 2x - 4y - 2 = 0
x
2
+
y
2
+
2
x
−
4
y
−
2
=
0
at the extremities of a diameter, then a.
c
=
−
4
c = -4
c
=
−
4
b.
g
+
f
=
c
−
1
g + f = c - 1
g
+
f
=
c
−
1
c.
g
2
+
f
2
−
c
=
17
g^2 + f^2 - c = 17
g
2
+
f
2
−
c
=
17
d.
g
f
=
6
gf = 6
g
f
=
6
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