If parabolas ${\mathrm{y}}^2=\mathrm{ax}$ and $25[{(\mathrm{x}-3)}^2+{(\mathrm{y}+2)}^2]={(3\mathrm{x}-4\mathrm{y}-2)}^2$ are equal then the value of a is ____

The parabolas are equal if the lengths of their latus rectum are equal. The length of latus rectum of ${\mathrm{y}}^2=\mathrm{ax}$ is a.
The equation of second parabola can be written as  $\sqrt{{(\mathrm{x}-3)}^2+{(\mathrm{y}+2)}^2}={\left(\frac{3\mathrm{x}-4\mathrm{y}-2}{5}\right)}^2$
Here focus is (3,-2) directrix is $3\mathrm{x}-4\mathrm{y}-2=0$
Length of the latus rectum =2 (distance between focus and directrix)
$=2\left|\frac{9-4(-2)-2}{\sqrt{9+16}}\right|=6$
The two parabolas are  equal if a=6