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

The equation of the image of the pair of lines $y = |x - 1|$ in the $y$-axis is:

If the products of the perpendiculars from the origin to the pairs of lines $xy+x+y+1=0$,$x^2-y^2+2x+1=0$,and $2x^2+3xy-2y^2+2x+1=0$ are $p_1, p_2$,and $p_3$ respectively,then:

The joint equation of the pair of lines passing through $(2,3)$ and parallel to the lines represented by $x^{2}-y^{2}=0$ is:

The joint equation of the straight lines $x + y = 1$ and $x - y = 4$ is

The value of $\lambda$ such that $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$ represents a pair of straight lines is: