Find the equation of a circle which touches the line 3x-4y+1=0 at (1,1) and which cuts the circle x^2+y^2-x=0 at (1,1)

Question

Find the equation of a circle which touches the line 3x-4y+1=0 at (1,1) and which cutx the circle x²+y²-x=0 at (1,1) and which cuts the circle x²+y²-x=0 orthogonally

Comments

(1,1) is not a point on the given circle. How will it be a point of intersection?. If answer is given , correction can be tried