Question 1141738
-64 is correct.
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For  {{{ Ax^2 + Bxy + Cy^2 + Dx + Ey = 0  }}}

rotated counter-clockwise by {{{theta}}}:


The leading coefficient in the rotated coordinates is:

A' = {{{ Acos^2(theta) + Bsin(theta)cos(theta) + Csin^2(theta) }}}

   = {{{ 11(1/2)^2 + (-50)(sqrt(3))(sqrt(3)/2) + (-39)(sqrt(3)/2)^2 }}}
 
   = {{{ (11 - 150 - 117) / 4 }}}