row[{x_,y_}]:={1,x,y,x*y,x^2,y^2};
DynamicModule[
{curve},
Manipulate[curve=With[
{eq=Det[Prepend[row/@{pt1, pt2, pt3, pt4, pt5},row[{x,y}]]]==0},
{Dynamic[ContourPlot[eq,
{x,-2,2},
{y,-2,2},
ImageSize->Medium
]]
}
];
curve,
{curve,None},
{{pt1,{1,0}},Locator},
{{pt2,{0,1}},Locator},
{{pt3,{-1,0}},Locator},
{{pt4,{0,-1}},Locator},
{{pt5,{0.7,0.7}},Locator}
]
]