Question

Consider a general equation of degree $2$, as $\lambda x^2-10xy+12y^2+5x-16y-3=0$

For the value of $\lambda$ obtained for the given equation to be a pair of straight lines, if $L_1=0$ and $L_2=0$ are the lines denoted by the given line pair then the product of the abscissa and ordinate of their point of intersection is

• A. $18$
• B. $28$
• C. $35$
• D. $25$

Answer 1

Answer: (C)

$35$

We have,

$2x^2-10xy+12y^2+5x-16y-3=0$

consider homogeneous equation

$2x^2-10xy+12y^2$

$(x-3y)(x-2y)$

$\therefore 2x^2-10xy+12y^2+5x-16y-3=0\equiv (2x-6y+A)(x-2y+B)$

upon solving the above equation, we get,

$A=-1,B=3$

hence lines are $2x-6y-1=0,x-2y+3=0$

upon solving intercept form, we get,

$(-10,-\frac{7}{2})$

$\therefore -10\times -\frac{7}{2}=35$