The extremities of lafus rectum of aparabola are (1, 1) and (1, -1). Then the equation of the parabola can be

Given that the  extremities  of the latus  rectum  are ( 1,1) (1, -1). Then,
$4\mathrm{a}=2$ and $\mathrm{a}=\frac{1}{2}$
Also, the focus of the parabola  is (1, 0).
Hence, the  vertex  can  be ( l/2,  0) or (3/2,  0).
Therefore,  the equations of the  parabola can be
${\mathrm{y}}^2=2\left(\mathrm{x}-\frac{1}{2}\right)$
or ${\mathrm{y}}^2=-2\left(\mathrm{x}-\frac{3}{2}\right)$
i.e., ${\mathrm{y}}^2=2\mathrm{x}-1$
or ${\mathrm{y}}^2=3-2\mathrm{x}$