Question 1027275
*[illustration gf3.JPG].
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Looks like the two positions marked in red are good candidates.
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Which would be the intersection of the ellipse and the line {{{y=x}}}.
Substituting,
{{{x^2+x^2+x^2=1}}}
{{{3x^2=1}}}
{{{x^2=1/3}}}
{{{x=0 +- 1/sqrt(3)}}}
{{{y=0 +- 1/sqrt(3)}}}
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*[illustration gf4.JPG].