The answer is the same as for these 2 spheres:
x^2 + y^2 + (z-0)^2 = 25 and
x^2 + y^2 + (z-6)^2 = 16
The cross section through the x-z plane is:
x^2 + (z-0)^2 = 25 and
x^2 + (z-6)^2 = 16
wlog, re-label z as y
25 - y^2 = 16 - (y-6)^2
25 - y^2 = 16 - y^2 + 12y - 36
12y = 45
y = 15/4
x^2 = 25 - 225/16 = 175/16
x = √(175/16) = (5/4)√7 =~ 3.307189
Going back to the z terminology and the original equations, one of the intersection points of the 2 spheres is:
((5/4)√7 - 2 , -3 , 7/4)
The radius of the intersecting circle is:
(5/4)√7 =~ 3.307189
https://www.desmos.com/calculator/kskqqxjs3h
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Posted by Larry
on 2024-10-04 12:48:48 |
Solution
