Question 306769
Coordinates of what exactly?
You can figure out which conic section it is by completing the square in x and y.
{{{3x^2+2y^2-12x-4y-136=0}}}
{{{3x^2-12x+2y^2-4y-136=0}}}
{{{3(x^2-4x)+2(y^2-2y)-136=0}}}
{{{3(x^2-4x+4)+2(y^2-2y+1)-136-12-2=0}}}
{{{3(x-2)^2+2(y-1)^2-150=0}}}
{{{(x-2)^2/2+(y-1)^2/3=150/6}}}
{{{(x-2)^2/2+(y-1)^2/3=25}}}
{{{(x-2)^2/50+(y-1)^2/75=1}}}
It's an ellipse centered at (2,1).
{{{ graph( 300, 300, -8, 10, -8, 10, 1-sqrt((25-(x-2)^2)/2),
1+sqrt((25-(x-2)^2)/2))) }}}