Plotting Particular Conic Section

Question

How would I plot $-2x^2 -2y^2 = 1$ on the x-y plane ? I believe it is an ellipse, since the coefficients have the same sign, I just don't know what the major and minor axes would be nor how to plot.

Answer 1

This equation is a degenerate conic : $$-2x^2-2y^2=1 \iff x^2+y^2 = -1/2$$ Can the sum of squares of two real numbers ever be negative ?

The set of points satisfying the given equation is therefore $\varnothing .$

Answer 2

It is an imaginary circle.

If $both$ coordinates are imaginary, the imaginary circle has a real radius = $1/\sqrt2$,

You cannot plot it on real axes.