If the origin is shifted to a point P by the translation of axes to remove the $y$-term from the equation…
If the origin is shifted to a point P by the translation of axes to remove the $y$-term from the equation $x^2-y^2+2 y-1$ $=0$. then the transformed equation of it is
$x^2-y^2=1$
$x^2-y^2=0$
$x^2+y^2=1$
$x^2+y^2=0$
Solution
$x^2+y^2+2 y-1=0$
let $x=X, y=Y+h \Rightarrow X^2-(Y+h)^2+2(Y+h)-1=0$
$\Rightarrow X^2-Y^2+2(1-h) Y-h^2+2 h-1=0$
To remove $y$-term, $h=1$
$\Rightarrow X^2-Y^2=0$ is the transformed equation