I am working on a homework question: What must be the value(s) of $c$ for the following equation to have exactly 1 solution?
The equation is of the standard form of the equation for an ellipse,
First I thought that there is no $c$ for which there is only one solution since an ellipse has infinitely many solutions. However, now I think if $c=0$ then there might only be one solution. However, I don't know how to prove this. Also, what if $ c <0 $? Will it still be an ellipse? Thanks.