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Question

Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax+2ay+c=0 and 5bx+2by+d=0 lies in the fourth quadrant and is equidistant from the two axes then

A
2bc3ad=0
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B
2bc+3ad=0
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C
3bc2ad=0
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D
3bc+2ad=0
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Solution

The correct option is B 3bc2ad=0
Solve the equations of two lines to get a point and satisfy it in the third equation of a line.

4ax+2ay+c=0 and 5bx+2by+d=0

Let the point of intersection be (k,k)

From both equations, we get

4ak2ak+c=0 , 5bk2bk+d=0

2ak+c=0 , 3bk+d=0

k=c2a , k=d3b

c2a=d3b

3bc2ad=0

Option C

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