Saved Bookmarks
| 1. |
If the equation `lambdax^2+ 4xy + y^2 + lambdax + 3y + 2 = 0` represent a parabola then find `lambda`.A. -4B. 4C. 0D. none of these |
|
Answer» Correct Answer - C Comparing the given equation with the general equation of second degree i.e. `ax^(2)+2hxy+by^(2)+2gx+2fy+c=0`, we have ltbtgt `a-lamda, b=1, c~~2, f=3/2, g=lamda/2 " and "h-2` `:." "Delta=abc+2fgh-of^(2)-bg^(2)-ch^(2)` `rArr" "Delta=2lamda=3lamda-(9lamda)/4-(lamda^(2))/4-8=-1/4(lamda^(2)-11lamda+32)` and, `h^(2)-ab=4-lamda`. If the given equation represents a parabola, we must have `Deltaneh^(2)" and "h^(2)=ab` Clearly, `lamda=4` sarisfies these two conditions. |
|