Question 1166142
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<pre>

Due to symmetry, it is clear that the intersection points (x,y) have |x| = |y|.


Then from the equations


    4x^2 + 9x^2 = 36

        13x^2   = 36

          x^2 = 36/13

      x = +/- {{{6/sqrt(13)}}},

      y = +/- {{{6/sqrt(13)}}}.


<U>ANSWER</U>.  The intersection points are  ({{{6/sqrt(13)}}},{{{6/sqrt(13)}}}),  ({{{-6/sqrt(13)}}},{{{6/sqrt(13)}}}),  ({{{6/sqrt(13)}}},{{{-6/sqrt(13)}}}),  ({{{-6/sqrt(13)}}},{{{-6/sqrt(13)}}}).
</pre>

Solved.