deletions | additions       diff --git a/When_e_1_e_2_e_3_R__.tex b/When_e_1_e_2_e_3_R__.tex  index 16df4a8..9b9c373 100644  --- a/When_e_1_e_2_e_3_R__.tex  +++ b/When_e_1_e_2_e_3_R__.tex 
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y_1^2+y_2^2+y_3^2-(t+R^2)^2=0  $$  $$  t = - R^2 \pm +  \sqrt{y_1^2+y_2^2+y_3^2} $$  Note: We consider the positive $t$. Negative $t$ corresponds to the point $\tilde{x}$ on the other side of the ellipsoid.