The equation `x^(3)+ax^(2)y+bxy^(2)+y^(3)=0` represents three straight lines, two of which are perpendicular, then the equation of the third line, isA. `y=ax`B. `y=bx`C. `y=x`D. `y=-x`

The equation `x^(3)+ax^(2)y+bxy^(2)+y^(3)=0` represents three straight

1.	The equation `x^(3)+ax^(2)y+bxy^(2)+y^(3)=0` represents three straight lines, two of which are perpendicular, then the equation of the third line, isA. `y=ax`B. `y=bx`C. `y=x`D. `y=-x`
Answer» Correct Answer - C Let `y=m_(1) x, y=m_(2)x and y=m_(3)x` be the lines represented by the given equation. Then, `x^(3)+ax^(2)y+bxy^(2)+y^(3)=(y-x_(1)x)(y-m_(2)x)(y-m_(3)x)` `rArr" "m_(1)+m_(2)+m_(3)=-a` `m_(1)m_(2)+m_(2)m_(3)+m_(3)m_(1)=b` and, `m_(1)m_(2)m_(3)=-1` Let `y=m_(1)x and y =m_(2)x` be perpendicular lines. Then, `m_(1)m_(2)=-1` `therefore" "m_(3)=1" "[because m_(1)m_(2)m_(3)=-1]` Thus, the third line is `y=m_(3)x` i.e., y = x.

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