Question

What is the equation of curve of intersection of sphere x^2+y^2+z^2=a^2 and x+z=a

Answer 1

use substitution
\[x^{2}+y^{2}+z^{2} = (x+z)^{2}\]
\[\rightarrow y^{2} = 2xz\]
z = a - x
\[y = \pm \sqrt{2x(a-x)}\]