SOLUTION: Hello, I am in a calculus course, and I am having difficulty solving this problem: Consider the circle C1: (x-1)^2+y^2=1, and the circle C2: x^2+y^2=r^2. For small r values, the

Question 268667: Hello, I am in a calculus course, and I am having difficulty solving this problem:
Consider the circle C1: (x-1)^2+y^2=1, and the circle C2: x^2+y^2=r^2. For small r values, the circles intersect. Consider the line that goes through the top of C2 and the intersection point in quadrant 1. As r->0, where does the root of the line tend to?
Thank you for the help!
J
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
OUr two equations are
(i)
(ii)
take (i) - (ii) to get
(iii)
simplify to get
(iv)
solving for x we get
(v)
now, we can find y as
(vi) y =
or simplified to
(vii) y =
Now, the y -intercept of C2 is (0,r).
---
Next we create an equation of a line passing through the y intercept of C2 and the crossing point of the two circles as
(viii) y =
We want the x intercept or the value of x when y = 0.
This is
(ix) x =
The limit of x as r -> 0, is 1
The root of the line tends to 1.
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