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AIEEE 2005 Math Solved Paper
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© examsnet.com
Question : 18
Total: 71
If the circles
x
2
+
y
2
+
2
a
x
+
c
y
+
a
=
0
and
x
2
+
y
2
−
3
a
x
+
d
y
−
1
=
0
intersect in two distinct points
P
and
Q
then the line
5
x
+
by
−
a
=
0
passes through
P
and
Q
for
exactly one value of
no value of a
infinitely many values of a
exactly two values of a
Validate
Solution:
s
1
=
x
2
+
y
2
+
2
a
x
+
c
y
+
a
=
0
s
2
=
x
2
+
y
2
−
3
a
x
+
d
y
−
1
=
0
Equation of common chord of circles
s
1
and
s
2
is
given by
s
1
−
s
2
=
0
⇒
5
a
x
+
(
c
−
d
)
y
+
a
+
1
=
0
Given that
5
x
+
b
y
−
a
=
0
passes through
P
and
Q
∴
The two equations should represent the same line
⇒
a
1
=
c
−
d
b
=
a
+
1
−
a
⇒
a
+
1
=
−
a
2
a
2
+
a
+
1
=
0
No real value of
a
.
© examsnet.com
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