Question

The following equations represents a pair of lines between $2x^2-xy-3y^2+19y-20=0$

• A. True
• B. False

Answer 1

The correct option is B False

Given equation of straight line is $2x^2-xy-3y^2+19y-20=0$

Comparing with $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ we get

$a=2,h=-\frac{1}{2},b=-3,g=0,f=\frac{19}{2},c=-20$

If the equation represents a pair of lines then,

$\left|\begin{array}{ccc}a& h& g\\ h& b& f\\ g& f& c\end{array}\right|=0$

$\Delta =\left|\begin{array}{ccc}2& -\frac{1}{2}& 0\\ -\frac{1}{2}& -3& \frac{19}{2}\\ 0& \frac{19}{2}& -20\end{array}\right|$

$=2(60-\frac{361}{4})+\frac{1}{2}(10-0)+0$

$=2\times \frac{120-361}{4}+5$

$=\frac{-241+10}{2}=\frac{-231}{2}\ne 0$

Since, determinant of the given equation is not zero, it does not represent a pair of lines.