Prove that a circle {x∈(C+∣=−1∣− 2
​
) in the s-plane oorresponds to a Sreat circle on the sphere S 2
undes the stereographic projection. Fecall on the phere S 3
={(x 1
​
,x 2
​
,x 3
​
)∈R 3
3x 2
+x 2
3
​
+x 3
3
​
=1), a groat eirele is determined y a linear equation a 1
​
x 1
​
+a 2
​
x 2
​
+a 3
​
x 3
​
=0. In the proof, yous need to find out 1. a 2
​
,a 3
​
explicitly. The sternographle paojection ls given by: γ −1
−1
:C+S 2
∣{(0,0,1)}∈R 3
⋅
(x,y)→( 1+x 2
+y 2
2x
​
⋅ 1+x 2
+y 2
2y
​
⋅ 1+x 2
+y 2
2 2
+y 2
−1
​
).
​