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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 : 50
Total: 88
A straight line cuts off the intercepts
OA
=
a
and
OB
=
b
on the positive directions of
x
-axis and
y
−
axis respectively. If the perpendicular from origin
O
to this line makes an angle of
π
6
with positive direction of
y
-axis and the area of
△
O
A
B
is
98
3
√
3
, then
a
2
−
b
2
is equal to:
[30-Jan-2023 Shift 1]
392
3
196
196
3
98
Validate
Solution:
Equation of straight line :
x
a
+
y
b
=
1
Or
x
cos
π
3
+
y
s
i
n
π
3
=
p
x
2
+
y
√
3
2
=
p
x
3
p
+
y
2
p
=
1
Comparing both :
a
=
2
p
,
b
=
2
p
√
3
Now area of
△
OAB
=
1
2
⋅
ab
=
98
3
⋅
√
3
1
2
⋅
2
p
⋅
2
p
√
3
=
98
3
⋅
√
3
p
2
=
49
a
2
−
b
2
=
4
p
2
−
4
p
2
3
=
2
3
4
p
2
=
8
3
⋅
49
=
392
3
© examsnet.com
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