Question 1024752
(a) Half as far from the origin;
is the more interesting question.  


Slope for the parallel line would be also 3/2, and the equation starts as  {{{3x-2y=c}}}
and then
{{{-2y=-3x+c}}}
{{{y=(3/2)x+c/(-2)}}}
or say as
{{{y=(3/2)x+b}}} and you do not yet know b.


How far is the GIVEN line from origin?
You need the perpendicular line containing the origin for this.
{{{y=-(2/3)x}}} is this perpendicular line.
WHERE does this line intersect with the given line of {{{3x-2y=26}}}?


{{{-2y=-3x+26}}}
{{{y=(3/2)x-13}}}


Find intersection point of {{{system(y=(3/2)x-13,y=-(2/3)x)}}}.
Intersection of the perpendicular lines is  (-4,6).


The line you want in question (a) will intersect or contain the MIDPOINT of  (0,0) and  (-4,6).
CAN YOU DO THE REST FROM HERE?