Question

If the equation $a{x}^2-6xy+y^2+2gx+2fy+c=0$ represents a pair of lines whose slopes are $m$ and $m^2$, Then sum of all possible values of a is

• A. 17
• B. - 19
• C. 19
• D. - 17

Answer 1

The correct option is B - 19

The given lines will be parallel to lines $a{x}^2-6xy+y^2=0$
So, ${\left(\frac{y}{x}\right)}^2-6\left(\frac{y}{x}\right)+a=0$
$m+m^2=6\dots \dots \left(1\right)$
which gives m = -3 or 2
and $m{m}^2=a\dots \dots \left(2\right)$
From (2) a = - 27 or 8
Hence sum of all possible value of a = -19