Answer:
r = 2.
Step-by-step explanation:
We can find the slope of the tangent using implicit differentiation:
x^2 + y^2 = r
2x + dy/dx * 2y = 0
dy/dx = -2x / 2y = -x/y = the slope of the tangent.
We have the line x + y = r
y = -x + r
This has a slope of -1 , so:
-x/y = -1
-x = -y
x = y
Substituting in x^2 + y^2 = r and x + y = r:-
2x^2 = r
2x = r
2x^2 - 2x = 0
2x(x - 1) = 0
x = 1
So r = 2x = 2.
