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JEE Main Math Class 11 Straight Lines and Pair of Straight Lines 1 Questions
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© examsnet.com
Question : 1
Total: 100
If
p
and
q
are the lengths of the perpendiculars from the origin on the lines,
x
c
o
s
e
c
α
−
y
sec
α
=
k
cot
2
α
and
x
sin
α
+
y
cos
α
=
k
sin
2
α
respectively, then
k
2
is equal to
[2021, 31 Aug. Shift-1]
4
p
2
+
q
2
2
p
2
+
q
2
p
2
+
2
q
2
2
p
2
+
q
2
p
2
+
4
q
2
Validate
Solution:
p
=
k
cot
2
α
√
c
o
s
e
c
2
α
+
sec
2
α
⇒
q
=
k
sin
2
α
√
sin
2
α
+
cos
2
α
⇒
p
=
k
(
cos
2
α
sin
2
α
)
√
sin
2
α
+
cos
2
α
sin
2
α
cos
2
α
=
k
cos
2
α
sin
2
α
⇒
p
=
(
k
2
)
cos
2
α
⇒
q
=
k
sin
2
α
⇒
cos
2
α
=
(
2
p
∕
k
)
⇒
sin
2
α
=
(
q
∕
k
)
⇒
sin
2
2
α
+
cos
2
2
α
=
1
⇒
4
p
2
k
2
+
q
2
k
2
=
1
⇒
4
p
2
+
q
2
=
k
2
© examsnet.com
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