The straight #y = 7/6x+1# can be represented as #(p-p_0).vec v =0#
where #p = (x,y), p_0 = (-1,0)# and #vec v = (7,-6)# and also can be represented in the parametric form as:
#S_1-> p = p_0+lambda* vec v^T# where #vec v^T# is the vector with components #(6,7)# which is orthogonal to #vec v#.
The center point to the circle is at the intersection of #S_1# and #S_2# where #S_2# is the mediatrix to the segment #bar(p_1p_2)#. #S_2# is written as:
#S_2->p = p_{12}+mu*vec v_{12}^T# where #p_{12} = (p_1+p_2)/2,vec v_{12} = p_1-p_2 = (1,-1)# and #vec v_{12}^T = {-1,-1}#.
Solving #p_0+lambda_c* vec v^T = p_{12}+mu_c*vec v_{12}^T# for #mu_c, lambda_c# we obtain #mu_c= -5, \lambda_c = 79/2#
Now, putting all together,
#p_c = p_0+lambda_c* vec v^T =(-31, -35) #
#r = norm(p_c-p_1)=sqrt[3121]#
