The equation `x^3-yx^2+x-y= 0` represents

Options

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

Answer

C

Explanation

We, have
`y^(2)-x^(2)+2x-1=0`
`rArr" "y^(2)-(x-1)^(2)=0`
`rArr" "(y+x-1)(y-x+1)=0rArry+x-1=0, y-x+1=0`
Hence, the given equation represents a pair of straight lines.
`ul("ALITER")` Comparing the given equation with
`ax^(2)+2hxy+by^(2)+2gx+2fy+c=0` we get
`a=-1,b=1,g=1, c=-1, f=h=0`
`therefore" "abc+2fgh-af^(2)-bg^(2)-ch^(2)=1+0-0-1-0=0`
Hence, the given equation represents a pair of straight lines.