Intersecting circles using Newton's Method

[Robb]

Homework Statement

Homework Equations

The Attempt at a Solution

My initial thought was to set the two equations equal to each other but the resulting equation is linear which gives a constant for a Newton iteration. I thought about Taylor's theorem in 2-d but I'm not so sure about that as far as deriving the iterating function. Please help!

 

[Mark44]

Homework Statement

View attachment 214649

Homework Equations

The Attempt at a Solution

My initial thought was to set the two equations equal to each other but the resulting equation is linear which gives a constant for a Newton iteration. I thought about Taylor's theorem in 2-d but I'm not so sure about that as far as deriving the iterating function. Please help!

Technically, you don't "set equations equal to each other." If you have one equation in the form f(x) = b and another equation in the form g(x) = b, then you can set f(x) equal to g(x). However, it makes no sense to write $(x - 2)^2 + (y - 1)^2 = 2 = 3.5 = (x - 2.5)^2 + y^2$.

For the equations in your problem, what you said amounts to setting 2 = 3.5, which is obviouly untrue.

What was the work that you did? You need to show us what you did, rather than just loosely describe your work, so that we can steer you in the right direction.

 

[Robb]

I have not chosen an initial condition yet so I can get F(X).