Question: A circle touches the lines $2x+3y+1=0$ at the point (1, -1) and is orthogonal to the circle which has the line segment having end points (0, -1) and (-2, 3) as the diameter. What is the equation of the circle?
Approach so far: Using the given coordinates of the line segment, the radius as well as the center of the circle can easily be calculated. However I am lost as how to proceed further. Please help!