after about 30 mins of typing my long detailed explanation, my internet went out and brainly timed out my answer and I was not able to copy my answer because of the time out notification so here is a shortened version of the answer (still correct but with much less explanation)
Using calculus
a line paralell to ax+by=c will be ax+by=d where a=a, b=b and d is a constant
so the paralell lines will have forms 4x+3y=d and 4x+3y=f
find implicit derivitive of circle function
[tex]\frac{dy}{dx}=\frac{2-x}{y-1}[/tex]
if we solve for where slope is equal to -4/3 (so that it is paralell to other line) we get
3x-4y=2, this is the equation of the line that passes through the circle at the 2 points where the 2 lines we want are
solving for x, we get x=(4y+2)/3
if we subsitute that for x in the circle equation, we get
y^2-2y-8=0
ergo y=-2 and y=4
subsitute that for y to find x in the x=(4y+2)/3 equation
when y=-2, x=-2
when y=4, x=6
now subsitute in to equations to find constants
4x+3y=d, find d
y=-2 and x=-2
4(-2)+3(-2)=d
-8-6=d
-14=d
4x+3y=-14 is one equation
4x+3y=f, find f
y=4, x=6
4(6)+3(4)=f
24+12=f
36=f
4x+3y=36 is another equation
the equations are
4x+3y=-14 and 4x+3y=36
