Verified answer

y + 8 = x(y+5)

y + 8 = xy + 5x

y - xy = 5x - 8

y (1-x) = 5x - 8

y = (5x - 8) / (1-x)

a = 5

b = -8

c = 1

The slope of y = x + a is a million. A tangent to a circle is often perpendicular to the radius on the factor of tangency. So the radius in question would desire to have slope -a million. because of the fact the middle is (4,a million) and the radius length is 4, the factor of tangency would desire to be the two (4 - 2sqrt2, a million + 2sqrt2) or (4 + 2sqrt2, a million - 2sqrt2). those are the only 2 factors that are distance 4 from the middle and mendacity alongside a line with slope -a million in the path of the middle. Plug each of those into y = x + a. in the 1st case, you get a = -3 + 4sqrt2 and in the 2nd case, a = -3 - 4sqrt2.

It helps to know that to make y the subject, expand all brackets

and the gather y's and xy's on one side and x's and numbers on the other

y+8 = x(y+5) = xy + 5x

y - xy =(1 - x)y =5x - 8

y =(5x - 8)/(1 - x)

compare with

y =(ax + b)/(c - x)

a = +5

b = -8

c = +1

Regards - Ian

if i am reading the question correctly

find the value of a

ax+b

-------- =y --------problem

c-x

ax+b=y(c-x) -----mutiply (c-x)

ax=y(c-x)-b ----------subtract b

y(c-x)-b

----------- = a

x

Find the value of b

ax+b

-------- =y -------problem

c-x

ax+b=y(c-x) --------mutilply (c-x)

b=y(c-x)-ax ------- subtract ax

Find the value of c

ax+b

-------- =y ---------problem

c-x

ax+b=y(c-x) -----mutiply (c-x)

ax+b

----------=c-x --------divide y

y

ax+b

---------- +x = c --------add x

y

Answers:

y(c-x)-b

----------- = a

x

b=y(c-x)-ax

ax+b

---------- +x = c

y