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Mathematics
Mathematics
Problem
If the points of intersection of the ellipses
x
2
+
2
y
2
−
6
x
−
12
y
+
23
=
0
x^2 + 2y^2 - 6x - 12y + 23 = 0
x
2
+
2
y
2
−
6
x
−
12
y
+
23
=
0
and
4
x
2
+
2
y
2
−
20
x
−
12
y
+
35
=
0
4x^2 + 2y^2 - 20x - 12y + 35 = 0
4
x
2
+
2
y
2
−
20
x
−
12
y
+
35
=
0
lie on a circle of radius
r
r
r
and centre
(
a
,
b
)
(a, b)
(
a
,
b
)
then the value of
a
b
+
18
r
2
ab + 18r^2
ab
+
18
r
2
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