Share
Explore BrainMass

Prove that the spheres x2 + y2 + z2 = 16 and x2+ (y+5)2 + z2 =9 intersect orthogonally.

Attachments

Solution Preview

find the point(s) of intersection:

the first equation implies x^2 + z^2 = 16 - y^2
and the second is x^2 + z^2 = 9 - (y -5)^2

so 16 - y^2 = 9 - (y - 5)^2 gives

16 - y^2 = 9 - y^2 + 10y - 25 ...

Solution Summary

It is proven that two spheres intersect orthogonally. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

$2.19