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Test Index
JEE Main Math Class 11 Straight Lines and Pair of Straight Lines 1 Questions
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© examsnet.com
Question : 98
Total: 100
Locus of mid point of the portion between the axes of
x
cos
α
+
y
sin
α
=
p
whre
p
is constant is
[2002]
x
2
+
y
2
=
4
p
2
x
2
+
y
2
=
4
p
2
1
x
2
+
1
y
2
=
2
p
2
1
x
2
+
1
y
2
=
4
p
2
Validate
Solution:
Equation of
A
B
is
x
cos
α
+
y
sin
α
=
p
;
⇒
x
cos
α
p
+
y
sin
α
p
=
1
⇒
x
p
∕
cos
α
+
y
p
∕
sin
α
=
1
So, co-ordinates of
A
and
B
are
(
p
cos
α
,
0
)
and
(
0
,
p
sin
α
)
So, coordinates of midpoint of
A
B
are
M
(
x
1
,
y
1
)
=
(
p
2
cos
α
,
p
2
sin
α
)
x
1
=
p
2
cos
α
&
y
1
=
p
2
sin
α
⇒
cos
α
=
p
∕
2
x
1
and
sin
α
=
p
∕
2
y
1
∵
cos
2
α
+
sin
2
α
=
1
Locus of
(
x
1
,
y
1
)
is
1
x
2
+
1
y
2
=
4
p
2
.
© examsnet.com
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