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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 : 53
Total: 88
A line, with the slope greater than one, passes through the point
A
(
4
,
3
)
and intersects the line
x
−
y
−
2
=
0
at the point
B
. If the length of the line segment
A
B
is
√
29
3
, then
B
also lies on the line:
[25-Jul-2022-Shift-1]
2
x
+
y
=
9
3
x
−
2
y
=
7
x
+
2
y
=
6
2
x
−
3
y
=
3
Validate
Solution:
Let inclination of required line is
θ
,
So the coordinates of point
B
can be assumed as
(
4
−
√
29
3
cos
θ
,
3
−
√
29
3
sin
θ
)
Which satisfices
x
−
y
−
2
=
0
4
−
√
29
3
cos
θ
−
3
+
√
29
3
sin
θ
−
2
=
0
sin
θ
−
cos
θ
=
3
√
29
By squaring
sin
2
θ
=
20
29
=
2
tan
θ
1
+
tan
2
θ
tan
θ
=
5
2
only (because slope is greater than 1 )
sin
θ
=
5
√
29
,
cos
θ
=
2
√
29
Point
B
:
(
10
3
,
4
3
)
Which also satisfies
x
+
2
y
=
6
© examsnet.com
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