Two parabolas have same focus namely at the point (3,-28). If their directories are the x-axis and y-axis respectively and slope of common chord is ‘t’ then $\left|\mathrm{t}\right|=$____

Equation of parabola whose directrix x-axis is
 ${(\mathrm{x}-3)}^2=-56(\mathrm{y}+14)$…..(1)
$2\mathrm{a}=28\Rightarrow \mathrm{a}=14$
Vertex =  (3,-14)
Directrix parallel to y-axis $\Rightarrow 2\mathrm{a}=3\Rightarrow \mathrm{a}=\frac{3}{2}$
Vertex $=\left(\frac{{\displaystyle 3}}{{\displaystyle 2}},-28\right)$
Equation of parabola is  ${(\mathrm{y}+28)}^2=6\left(\mathrm{x}-\frac{{\displaystyle 3}}{{\displaystyle 2}}\right)$….(2)
Solving (1), (2) we get $\mathrm{y}=\pm \mathrm{x}$
$\left|\mathrm{t}\right|=1$