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WBJEE 2012 Math Solved Paper
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© examsnet.com
Question : 66
Total: 80
A straight line through the point of intersection of the lines
x
+
2
y
=
4
and
2
x
+
y
=
4
meets the coordinate axes at A and B. The locus of the mid-point of AB is
3
(
x
+
y
)
=
2
x
y
2
(
x
+
y
)
=
3
x
y
2
(
x
+
y
)
=
x
y
x
+
y
=
3
x
y
Validate
Solution:
Given lines are
x
+
2
y
=
4
....(i)
and
2
x
+
y
=
4
...(ii)
Solving Eqs. (i) and (ii), we get
x
=
4
3
,
y
=
4
3
Let
A
B
:
x
a
+
y
b
=
1
...(iii)
Meets x-axis at A and y-axis at B
If the straight line (iii) passes through the point
(
4
3
,
4
3
)
, then
4
3
a
+
4
3
b
=
1
1
a
+
1
b
=
3
4
...(iv)
Let the mid-point of AB be
(
h
,
k
)
h
=
a
+
0
2
,
k
=
0
+
b
2
⇒
a
=
2
h
,
b
=
2
k
∴ From Eq. (iv)
1
2
h
+
1
2
k
=
3
4
⇒
2
h
+
2
k
=
3
h
k
Replace x, y from h, k respectively, we get required locus
i.e.,
2
(
x
+
y
)
=
3
x
y
© examsnet.com
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