Question

The second degree equation $6x^2+17xy+12y^2+22x+31y+20=0$ represents

• A. pair of lines
• B. a parabola
• C. an ellipse
• D. none of these

Answer 1

The correct option is A pair of lines

The equation $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ represent pair of lines, if $abc+2ghf-a{f}^2-b{g}^2-c{h}^2=0$.
Given equation $6x^2+17xy+12y^2+22x+31y+20=0$, we get the value of equation $abc+2ghf-a{f}^2-b{g}^2-c{h}^2=0$

$\Rightarrow \left(6\right)\left(12\right)\left(20\right)+2\left(11\right)\left(\frac{17}{2}\right)\left(\frac{31}{2}\right)-6\left({\frac{31}{2}}^2\right)-12\left({11}^2\right)-20.{\left(\frac{17}{2}\right)}^2=0$.
Therefore, given equation represent pair of lines.