If the equation `x^(4)+bx^(3)y+cx^(2)y^(2)+dxy^(3)+ey^(4)=0` represent two pairs of perpendicular lines, thenA. `b+d=1 and e=-1`B. `b+d=0 and e=-1`C. `b+d=0 and e=1`D. none of these

If the equation `x^(4)+bx^(3)y+cx^(2)y^(2)+dxy^(3)+ey^(4)=0` represent

1.	If the equation `x^(4)+bx^(3)y+cx^(2)y^(2)+dxy^(3)+ey^(4)=0` represent two pairs of perpendicular lines, thenA. `b+d=1 and e=-1`B. `b+d=0 and e=-1`C. `b+d=0 and e=1`D. none of these
Answer» Correct Answer - B Let `x^(2)+alpha xy-y^(2)=0 and x^(2)+beta xy-y^(2)=0` be two pairs of perpendicular lines given by the equation `x^(4)+bx^(3)y+cx^(2)y^(2)+dxy^(3)+ey^(4)=0`. Then, `x^(4)+bx^(3)y+cx^(2)y^(2)+dxy^(3)+ey^(4)=(x^(2)+alpha xy-y^(2))(x^(2)+beta xy-y^(2))` On equating the coefficients of like terms, we get `e=-1, b=beta+alpha, c=alpha beta and d=-beta-alpha` `rArr" "b+d=-, e=-1`

The lines represented by the equation `ax^(2)+2bxy+hy^(2)=0` are mutually perpendicular ifA. `a+b=0`B. `b+h=0`C. `h+a=0`D. `ah=-1`
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