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Question

A variable line is drawn through the intersection point of the lines 3x+4y12=0 and x+2y5=0 meeting the coordinate axes at the points A and B. Locus of mid point of segment AB is

A
4x+3y=4xy
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B
3x+4y=3xy
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C
3x+4y=4xy
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D
none
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Solution

The correct option is B 3x+4y=4xy
REF.Image
Integration of (3x+4y12=0&x+2y=5)
x=52y
3x+4y=12
3(52y)+4y=12
156y+4y=12
2y=3y=3/2
x=2
Intersection pt. (2,3/2)
eqn. of line : y=mx+c
32=2m+cc=322m
y=mx+cx=0y=c
k=c
y=mx+cy=0x=c/m
h=c/m
Mid pt. of (h,0)&(0,k) is (h/2,k/2)
(h2,k2)(c2m,c2)=(2m3/22m,3/22m2)
=(134m,34m)=(h,k)
h=13/4m34m=1hm=34(1h)
k=34mm=(34k)
m=34(1h)=34k31h=34k
3=3(1h)4k(1h)3h+4k=4hk
3x+4y=4xy

1382163_1211888_ans_395d58a9897b440aa1c80ae6f96b75d9.PNG

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