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JEE Main Math Class 11 Straight Lines and Pair of Straight Lines 2 Questions
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© examsnet.com
Question : 31
Total: 88
Let
A
(
0
,
1
)
,
B
(
1
,
1
)
and
C
(
1
,
0
)
be the mid-points of the sides of a triangle with incentre at the point
D
. If the focus of the parabola
y
2
=
4
ax
passing through
D
is
(
α
+
β
√
3
,
0
)
, where
α
and
β
are rational numbers, then
α
β
2
is equal to
[8-Apr-2023 shift 2]
6
8
9
2
12
Validate
Solution:
a
=
OP
=
2
b
=
OQ
=
2
c
=
PQ
=
2
√
2
D
(
4
2
+
2
+
2
√
2
,
4
2
+
2
+
2
√
2
)
≡
D
(
2
2
+
√
2
,
2
2
+
√
2
)
y
2
=
4
ax
⇒
(
2
2
+
√
2
)
2
=
4
a
⋅
(
2
2
+
√
2
)
∴
4
a
=
2
2
+
√
2
∴
a
=
1
2
⋅
2
−
√
2
4
−
2
=
1
4
(
2
−
√
2
)
∴
α
=
2
4
=
1
2
β
=
−
1
4
∴
α
β
2
=
8
Ans.
© examsnet.com
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