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Question

If the lines represented by ax2+8xy+3y2=0 are mutually perpendicular, then

A
x3y=0 is one of the line representing pair of lines
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B
|a|=3
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C
y3x=0 is one of the line representing pair of lines
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D
|a|=83
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Solution

The correct options are
A x3y=0 is one of the line representing pair of lines
B |a|=3
The lines given by ax2+5xy+3y2=0 are mutually perpendicular if
coefficient of x2 + coefficient of y2=0
a+3=0
a=3
|a|=3
Now 3x2+8xy+3y2=0
3x2+9xyxy+3y2=0(3yx)(y+3x)=0
So the lines will be
x=3y; y+3x=0

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