Question 1040552
The tangent line is perpendicular to a radius.  You want to know the line's equation having slope  {{{1/4}}} passing through the given center (-4,3).  This is   {{{y-3=(1/4)(x+4)}}}
{{{y-3=x/4+1}}}
{{{y=x/4+4}}}



A point ON the circle is the intersection of  {{{system(y=x/4+4,and,y=-4x-30)}}}.


How far is this intersection from the center of the circle  (-4,3)?
Distance Formula, giving this radius.


Do still need more help?