Answer
$${\text{Is not a conic}}$$
Work Step by Step
$$\eqalign{
& 6{x^2} - 12x + 6{y^2} - 18y + 25 = 0 \cr
& {\text{Subtract 25 from both sides}} \cr
& 6{x^2} - 12x + 6{y^2} - 18y = - 25 \cr
& {\text{Factor}} \cr
& 6\left( {{x^2} - 2x} \right) + 6\left( {{y^2} - 3y} \right) = - 25 \cr
& {\text{Complete the square and factor}} \cr
& 6\left( {{x^2} - 2x + 1} \right) + 6\left( {{y^2} - 3y + \frac{9}{4}} \right) = - 25 + 6\left( 1 \right) + 6\left( {\frac{9}{4}} \right) \cr
& 6{\left( {x - 1} \right)^2} + 6{\left( {y - \frac{3}{2}} \right)^2} = - \frac{{11}}{2} \cr
& {\text{Therefore, the graph dones not represent a Conic}} \cr} $$
