Question

The equation $y^2-x^2+2x-1=0$ represents

• A. a hyperbola
• B. a ellipse
• C. a pair of straight lines
• D. a rectangular hyperbola

Answer 1

Answer: (C)

a pair of straight lines

The given equation is,
$y^2-x^2+2x-1=0$ ........ (i)
Compare it with the general equation of second degree conic section i.e.,
$a{x}^2+2hxy+p{y}^2+2gx+2fy+c=0$ ... (ii)
we get, $a=-1,b=1,c=-1,h=0,g=1$ and f$f=0$
$\therefore$ Discriminant $=\Delta =abc+2fgh-af{f}^2-b{g}^2-c{h}^2$
$=(-1)\left(1\right)(-1)+2\left(0\right)\left(1\right)\left(0\right)-0-1=0$
Hence, the given equation will represent a pair of straight lines.