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# The equation $2x^2+3y^2-8x-18y+35=k$ represents

$\begin{array}{1 1}(A)\;\text{no locus if k >0} \\(B)\;\text{an ellipse if k <0 } \\(C)\;\text{ a point if k=0} \\(D)\;\text{a hyperbola if k >0} \end{array}$

We have $2x^2+3y-8x-18y+35=k$
=> $2 (x^2-4x)+3(y^2-6y+35)=k$
=>$2(x-2)^2+3(y-3)^2=k$
For $k=0$ we get $2(x-2)^2 +3(y-3)^2=0$
Which represents the point $(2,3)$
Hence C is the correct answer.