Question 1016038
Create two lines that are parallel to the tangent line.
These two lines will be 5 units away from the tangent line, one above, one below.
Once you have those lines, you can find the intersection point of those lines with {{{x=2}}} to find the center of the circles. 
The tangent line is
{{{3x-4y+11=0}}
{{{4y=3x+11}}}
{{{y=(3/4)x+11/4}}}
You can calculate the difference in y-intercepts given the distance, d, between parallel lines using the formula,
{{{d=DELTA*b/sqrt(m^2+1)}}}
{{{5=DELTA*b/sqrt((3/4)^2+1)}}}
{{{DELTA*b=sqrt(25/16)*5}}}
{{{DELTA*b=(5/4)*5}}}
{{{DELTA*b=25/4}}}
So the two lines would be,
{{{y[1]=(3/4)x+11/4+25/4=(3/4)x+36/4=(3/4)x+9}}}
{{{y[2]=(3/4)x+11/4-25/4=(3/4)x-14/4=(3/4)x-7/2}}}
So when {{{x=2}}},
{{{y[1]=(3/4)2+9=3/2+18/2=21/2}}}
{{{y[2]=(3/4)2-7/2=3/2-7/2=-2}}}
So then the circles are,
{{{(x-2)^2+(y-21/2)^2=25}}} and
{{{(x-2)^2+(y+2)^2=25}}}
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*[illustration dc21.JPG].