#color(blue)("Building the initial condition model")#
Let some constant related to #x# be #K_x#
Let some constant related to #y# be #K_y#
Let the radius be #r#
#color(green)("Then as a general equation we have:")#
#color(green)((x-K_x)^2+(y-K_y)^2=r^2" "......................Equation(1))#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
For point 1 #->P_1 ->(-4,3)" "Equation(1)# becomes:
#(-4-K_x)^2+(3-K_y)^2=r^2#
#(K_x)^2+8K_x+16+(K_y)^2-6K_y+9=r^2#
#color(brown)((K_x)^2+(K_y)^2+8K_x-6K_y+25=r^2color(white)("ddd")Eqn(1_a))#
......................................................................................
For point 2 #->P_2->(3,4)" "Equation(1)# becomes:
#(3-K_x)^2+(4-K_y)^2=r^2#
#(K_x)^2-6K_x+9+(K_y)^2-8K_y+16=r^2#
#color(brown)((K_x)^2 +(K_y)^2-6K_x-8K_y+25=r^2color(white)("ddd")Eqn(1_b) )#
...........................................................................
For point 3 #->P_2->(3,4)" "Equation(1)# becomes:
#(5-K_x)^2+(0-K_y)^2=r^2#
#(K_x)^2 -10K_x+25+(K_y)^2=r^2 #
#color(brown)((K_x)^2+(K_y)^2-10K_x+25=r^2color(white)("ddd") Eqn(1_c)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#
#color(brown)((K_x)^2+(K_y)^2+8K_x-6K_y+25=r^2color(white)("ddd")Eqn(1_a))#
#color(brown)((K_x)^2 +(K_y)^2-6K_x-8K_y+25=r^2color(white)("ddd")Eqn(1_b) )#
#color(brown)((K_x)^2+(K_y)^2-10K_xcolor(white)("ddddd")+25=r^2color(white)("ddd") Eqn(1_c)#
Now you manipulate these to gradually isolate the unknowns.
3 unknowns and 3 equations so solvable.
