Intersection of 2 Circle Equations

[Jake West]

I am aware that the equation of a circle is:

(x−h)^2+(y−k)^2=r^2.

I am looking to find a point on a globe where east/west and north/south meet.

Is there a correct way to mathematically describe an equation that involves the intersection of 2 circles (E/W and N/S)?

Any suggestions? Thanks in advance for any help that you may offer!

 

[lex]

Circle-Circle Intersection -- from Wolfram MathWorld

Two circles may intersect in two imaginary points, a single degenerate point, or two distinct points. The intersections of two circles determine a line known as the radical line. If three circles mutually intersect in a single point, their point of intersection is the intersection of their...

mathworld.wolfram.com

 

[Jake West]

Thank you so much for your reply! I will learn a lot from this

 

[lex]

It’s a bit complicated, but hopefully you can pick out the bits in the middle that are understandable and of use to you.