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If 16l^2+9m^2=24lm+6l+8m+1 and the line...

If `16l^2+9m^2=24lm+6l+8m+1` and the line `mx+ly=1` is tangent to circle `S_1=0` then the equation of circle `S_2=0` which touches `S_1=0` at `(0,0)` and passing `(3,1)` is given by `x^2+y^2-ax-by+c=0,` then find the value of `sqrt(3a+4b+5c)`

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