Question 1015551
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please help me graph 3x^2 + 4y^2 -6x -24y +39=0
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Complete squares in x and y:

{{{3x^2 + 4y^2 -6x -24y +39}}} = {{{3((x-1)^2 - 1) + 4((y-3)^2 - 9) + 39}}} = {{{3(x-1)^2 + 4(y-3)^2 + 39 - 3 - 36}}} = {{{3(x-1)^2 + 4(y-3)^2}}}.

So, your equation is

{{{3(x-1)^2 + 4(y-3)^2}}} = {{{0}}},   or

{{{3(x-1)^2}}} = {{{-4(y-3)^2}}}.

This equation has the unique solution: x =1 and y=3.
There is no other real solutions.

So, the equation describes only one point (1,3).

The plot consists of only one point (1,3).
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