If the lines represented by ax2+8xy+3y2=0 are mutually perpendicular, then
A
x−3y=0 is one of the line representing pair of lines
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B
|a|=3
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C
y−3x=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 Ax−3y=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 ofx2+coefficient ofy2=0 ⇒a+3=0 ⇒a=−3 ∴|a|=3 Now −3x2+8xy+3y2=0 ⇒−3x2+9xy−xy+3y2=0⇒(3y−x)(y+3x)=0 So the lines will be x=3y;y+3x=0