The centre of the circle x2+y2−3x−4y−1=0 is C(3/2,2), now as it is given that the required circle passes through the point C(3/2,2) and having centre (5,2), so radius of required circle is
r=√(5−‌
3
2
)2+(2−2)2=‌
7
2
∴ Equation of required circle is (x−5)2+(y−2)2=(‌