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Test Index
JEE Main Math Class 11 Straight Lines and Pair of Straight Lines 2 Questions
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© examsnet.com
Question : 19
Total: 88
If the sum of squares of all real values of
α
, for which the lines
2
x
−
y
+
3
=
0
,
6
x
+
3
y
+
1
=
0
and
α
x
+
2
y
−
2
=
0
do not form a triangle is
p
, then the greatest integer less than or equal to
p
is .........
[27-Jan-2024 Shift 2]
Your Answer:
Validate
Solution:
👈: Video Solution
2
x
−
y
+
3
=
0
6
x
+
3
y
+
1
=
0
α
x
+
2
y
−
2
=
0
Will not form a
∆
if
α
x
+
2
y
−
2
=
0
is concurrent with
2
x
−
y
+
3
=
0
and
6
x
+
3
y
+
1
=
0
or parallel to either of them so
Case-1: Concurrent lines
|
2
−
1
3
6
3
1
α
2
−
2
|
=
0
⇒
α
=
4
5
Case-2 : Parallel lines
−
α
2
=
−
6
3
or
−
α
2
=
2
⇒
α
=
4
or
α
=
−
4
P
=
16
+
16
+
16
25
[
P
]
=
[
32
+
16
25
]
=
32
© examsnet.com
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