All you need is to find the coordinates of the center of the circle, i.e. the intersection point of the given lines.


For it, you need to solve the system of linear equations


     x +  y =  4,    (1)

    5x + 2y = -1.    (2)


From equation (1), express y = 4-x  and substitute it into equation (2).  You will get single equation for x


    5x + 2*(4-x) = -1,

    5x + 8 - 2x = -1

       3x       = -1 - 8

       3x       = -9

        x       = -9/3 = -3.


Now from equation (1)  y = 4 - x = 4 - (-3) = 4 + 3 = 7.


The center point is  (-3,7);  the standard form circle equation is


     +  = ,

or

     +  = 25.    ANSWER