Question 932193
First find the centers.
{{{x^2-10x+y^2-10y+49=0}}}
{{{(x^2-10x+25)+(y^2-10y+25)+49=25+25}}}
{{{(x-5)^2+(y-5)^2=1}}}
({{{5}}},{{{5}}}) with a radius of {{{1}}}.
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{{{x^2-4x+y^2-6y+9=0}}}
{{{(x^2-4x+4)+(y^2-6y+9)+9=4+9}}}
{{{(x-2)^2+(y-3)^2=4}}}
({{{2}}},{{{3}}}) with a radius of {{{2}}}.
Find the slope,
{{{m=(5-3)/(5-2)=2/3}}}
Use the point-slope form,
{{{y-5=(2/3)(x-5)}}}
{{{y-5=(2/3)x-10/3}}}
{{{y=(2/3)x-10/3+15/3}}}
{{{highlight(y=(2/3)x+5/3)}}}
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{{{drawing(300,300,-2,10,-2,10,grid(1),circle(5,5,0.2),circle(2,3,0.2),
circle(5,5,1),circle(2,3,2),graph(300,300,-2,10,-2,10,(2/3)x+5/3))}}}