I'm confused by this question:
If $f(x) = 2x^2 - 6y^2+xy+2x-17y-12=0$ is to represent a pair of straight lines, one of which has equation $x+2y+3=0$, what must be the equation of the other line? Verify that $f(x)=0$ does, indeed, represent a pair of straight lines.
Given the general form of a conic section $Ax^2+By^2+Cxy+Dx+Ey+F=0$ we know that if $C^2 > 4AC$ as here, it's a hyperbola. Therefore I don't get how the equation can represent 2 straight lines. Any clues?