Question 1024962
There must be a less painful way to do this.
 
The distance from (a,b) to (6,3) is
{{{sqrt((a-6)^2+(b-3)^2)=5}}} , so
{{{(a-6)^2+(b-3)^2=25}}}
 
{{{5a-4b=14}}} because point (a,b) ies on the line {{{5x - 4y = -14}}} .
{{{5a-4b=14}}} --> {{{b=(5/4)a+7/2}}} --> {{{b-3=(5/4)a+1/2}}} --> {{{(b-3)^2=(25/16)a^2+(5/4)a+1/4}}}
 
Substituting that expression in {{{(a-6)^2+(b-3)^2=25}}} we get
{{{(a-6)^2+(25/16)a^2+(5/4)a+1/4=25}}}
{{{a^2-12a+36+(25/16)a^2+(5/4)a+1/4=25}}}
Multiplying both sides of the equal sign times {{{16}}} , we get
{{{16a^2-192a+576+25a^2+20a+4=400}}}-->{{{41a^2-172a+180=0}}}
Applying the quadratic formula, we get
{{{a = (-(-172) +- sqrt((-172)^2-4*41*180 ))/(2*41) }}}
{{{a = (172 +- sqrt(29584-29520))/82}}}
{{{a = (172 +- sqrt(64))/82}}}
{{{a = (172 +- 8)/82}}}--->{{{system(a=(172-8)/82=164/82=2,"or",a=(172+8)/82=180/82=highlight(90/41))}}}