WBJEE 2012 Math Solved Paper

Given lines are
x+2y=4....(i)
and 2x+y=4...(ii)
Solving Eqs. (i) and (ii), we get
x=‌

4

3

,y=‌

4

3

Let AB:‌

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

3a

+

4

3b

=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=2h,b=2k
∴ From Eq. (iv) ‌

1

2h

+‌

1

2k

=‌

3

4

⇒2h+2k=3hk
Replace x, y from h, k respectively, we get required locus
i.e., 2(x+y)=3xy